cpp-library

This documentation is automatically generated by competitive-verifier/competitive-verifier

View the Project on GitHub shino16/cpp-library

:heavy_check_mark: test/ps/fps.log.test.cpp

Depends on

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/log_of_formal_power_series

#include "mod/modint.hpp"
#include "io.hpp"
#include "ps/fps.hpp"
using mint = atcoder::modint998244353;
using fps = formal_power_series<mint>;

int main() {
  int n = in;
  fps f(in.vec<mint>(n));
  f = move(f).log(n);
  out.iter(all(f));
}

#line 1 "test/ps/fps.log.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/log_of_formal_power_series

#line 1 "mod/modint.hpp"



#include <cassert>
#include <numeric>
#include <type_traits>

#ifdef _MSC_VER
#include <intrin.h>
#endif

#line 1 "atcoder/internal_math.hpp"



#include <utility>

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    unsigned long long im;

    // @param m `1 <= m < 2^31`
    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    // @return m
    unsigned int umod() const { return _m; }

    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        // [1] m = 1
        // a = b = im = 0, so okay

        // [2] m >= 2
        // im = ceil(2^64 / m)
        // -> im * m = 2^64 + r (0 <= r < m)
        // let z = a*b = c*m + d (0 <= c, d < m)
        // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
        // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
        // ((ab * im) >> 64) == c or c + 1
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};

    // Contracts:
    // [1] s - m0 * a = 0 (mod b)
    // [2] t - m1 * a = 0 (mod b)
    // [3] s * |m1| + t * |m0| <= b
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b

        // [3]:
        // (s - t * u) * |m1| + t * |m0 - m1 * u|
        // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        // = s * |m1| + t * |m0| <= b

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    // by [3]: |m0| <= b/g
    // by g != b: |m0| < b/g
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
                                      unsigned long long m,
                                      unsigned long long a,
                                      unsigned long long b) {
    unsigned long long ans = 0;
    while (true) {
        if (a >= m) {
            ans += n * (n - 1) / 2 * (a / m);
            a %= m;
        }
        if (b >= m) {
            ans += n * (b / m);
            b %= m;
        }

        unsigned long long y_max = a * n + b;
        if (y_max < m) break;
        // y_max < m * (n + 1)
        // floor(y_max / m) <= n
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

}  // namespace internal

}  // namespace atcoder


#line 1 "atcoder/internal_type_traits.hpp"



#line 7 "atcoder/internal_type_traits.hpp"

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder


#line 14 "mod/modint.hpp"

namespace atcoder {

namespace internal {
struct modint_base {}; struct static_modint_base : modint_base {}; template <class T> using is_modint = std::is_base_of<modint_base, T>; template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
  using mint = static_modint; public: static constexpr int mod() { return m; } static constexpr mint raw(int v) { mint x; x._v = v; return x; } constexpr static_modint() : _v(0) {} template <class T, internal::is_signed_int_t<T>* = nullptr> constexpr static_modint(T v) : _v() { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template <class T, internal::is_unsigned_int_t<T>* = nullptr> constexpr static_modint(T v) : _v() { _v = (unsigned int)(v % umod()); } constexpr unsigned int val() const { return _v; } constexpr mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } constexpr mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } constexpr mint operator++(int) { mint result = *this; ++*this; return result; } constexpr mint operator--(int) { mint result = *this; --*this; return result; } constexpr mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } constexpr mint& operator-=(const mint& rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } constexpr mint& operator*=(const mint& rhs) { unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } constexpr mint operator+() const { return *this; } constexpr mint operator-() const { return mint() - *this; } constexpr mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } constexpr mint inv() const { if (prime) { assert(_v); return pow(umod() - 2); } else { auto eg = internal::inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } constexpr friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } constexpr friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } constexpr friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } constexpr friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } constexpr friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } constexpr friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } constexpr friend bool operator<(const mint& lhs, const mint& rhs) { return lhs._v < rhs._v; } private: unsigned int _v; static constexpr unsigned int umod() { return m; } static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
  using mint = dynamic_modint; public: static int mod() { return (int)(bt.umod()); } static void set_mod(int m) { assert(1 <= m); bt = internal::barrett(m); } static mint raw(int v) { mint x; x._v = v; return x; } dynamic_modint() : _v(0) {} template <class T, internal::is_signed_int_t<T>* = nullptr> dynamic_modint(T v) { long long x = (long long)(v % (long long)(mod())); if (x < 0) x += mod(); _v = (unsigned int)(x); } template <class T, internal::is_unsigned_int_t<T>* = nullptr> dynamic_modint(T v) { _v = (unsigned int)(v % mod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v += mod() - rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator*=(const mint& rhs) { _v = bt.mul(_v, rhs._v); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { auto eg = internal::inv_gcd(_v, mod()); assert(eg.first == 1); return eg.second; } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } friend bool operator<(const mint& lhs, const mint& rhs) { return lhs._v < rhs._v; } private: unsigned int _v; static internal::barrett bt; static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {
template <class T> using is_static_modint = std::is_base_of<internal::static_modint_base, T>; template <class T> using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>; template <class> struct is_dynamic_modint : public std::false_type {}; template <int id> struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {}; template <class T> using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
}  // namespace internal

}  // namespace atcoder


#line 2 "prelude.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using vll = vector<ll>;
using vvll = vector<vector<ll>>;
using vc = vector<char>;
#define rep2(i, m, n) for (auto i = (m); i < (n); i++)
#define rep(i, n) rep2(i, 0, n)
#define repr2(i, m, n) for (auto i = (n); i-- > (m);)
#define repr(i, n) repr2(i, 0, n)
#define all(x) begin(x), end(x)
auto ndvec(int n, auto e) { return vector(n, e); }
auto ndvec(int n, auto ...e) { return vector(n, ndvec(e...)); }
auto comp_key(auto&& f) { return [&](auto&& a, auto&& b) { return f(a) < f(b); }; }
auto& max(const auto& a, const auto& b) { return a < b ? b : a; }
auto& min(const auto& a, const auto& b) { return b < a ? b : a; }
#if __cpp_lib_ranges
namespace R = std::ranges;
namespace V = std::views;
#endif
#line 3 "io.hpp"

template <size_t BufSize = 1 << 26> class stdin_reader {
 public: stdin_reader() { buf[fread(buf, 1, sizeof(buf), stdin)] = 0; } template <class T> enable_if_t<is_integral_v<T>> read(T& x) { skip(); [[maybe_unused]] bool neg = false; if constexpr (is_signed_v<T>) neg = *p == '-' ? (p++, true) : false; x = 0; while (*p > ' ') x = x * 10 + (*p++ & 0x0F); if constexpr (is_signed_v<T>) x = neg ? -x : x; } template <class T> void_t<decltype(&T::val)> read(T& x) { x = T((unsigned)(*this)); } void read(char &c) { skip(); c = *p++; } void read(char*& q) { skip(); q = p; while (*p > ' ') p++; *p = 0; } template <size_t N> void read(char (&s)[N]) { read(s); } void read(string& s) { skip(); char* p0 = p; while (*p > ' ') p++; s.assign(p0, p); } template <class T, void_t<decltype(tuple_size<T>::value)>* = nullptr> void read(T& x) { read_tuple_impl(x, make_index_sequence<tuple_size_v<T>>{}); } template <class T, class U> void read(pair<T, U>& x) { read(x.first), read(x.second); } template <class T, size_t N> void read(T (&a)[N]) { for (auto& e : a) read(e); } template <class T> operator T() { T x; return read(x), x; } template <class... Ts> void operator()(Ts&... xs) { (read(xs), ...); } int operator--() { return (int)*this - 1; } template <class T> T* arr(int n) { T* p = new T[n + 1]; rep(i, n) read(p[i]); return p; } template <class T> void vec(vector<T>& v, int n) { v.resize(n); for (auto& e : v) read(e); } template <class T> vector<T> vec(int n) { vector<T> v; return vec(v, n), v; } auto vi(int n) { return vec<int>(n); } auto vi1(int n) { auto v = vec<int>(n); rep(i, n) v[i]--; return v; } auto vll(int n) { return vec<ll>(n); } template <class... Ts> tuple<vector<Ts>...> vecs(int n) { tuple<vector<Ts>...> res; vecs_impl(res, n, make_index_sequence<sizeof...(Ts)>{}); return res; } template <class T> void vvec(vector<vector<T>>& v, int n, int m) { v.resize(n); for (auto& e : v) vec(e, m); } template <class T> vector<vector<T>> vvec(int n, int m) { vector<vector<T>> v; return vvec(v, n, m), v; } template <class... Ts> auto cols(int n) { return transpose(vec<tuple<Ts...>>(n)); } private: char buf[BufSize], *p = buf; void skip() { while (*p <= ' ') p++; } template <class T, size_t... Is> void read_tuple_impl(T& x, index_sequence<Is...>) { (*this)(get<Is>(x)...); } template <class T, size_t... Is> void vecs_impl(T& x, int n, index_sequence<Is...>) { (vec(get<Is>(x), n), ...); } template <class T, size_t... Is> static auto transpose_impl(const vector<T>& v, index_sequence<Is...>) { tuple<vector<decay_t<tuple_element_t<Is, T>>>...> w; (get<Is>(w).reserve(v.size()), ...); for (const auto& row : v) (get<Is>(w).push_back(get<Is>(row)), ...); return w; } template <class T> static auto transpose(const vector<T>& v) { return transpose_impl(v, make_index_sequence<tuple_size_v<T>>{}); }
};
template <size_t BufSize = 1 << 26> class stdout_writer {
 public: ~stdout_writer() { flush(); } void flush() { fwrite(buf, 1, p - buf, stdout), p = buf; } void write_char(char c) { *p++ = c; } void write() {} void write(char c) { write_char(c); } template <class T> enable_if_t<is_integral_v<T>> write(T x) { if (!x) return write_char('0'); if constexpr (is_signed_v<T>) if (x < 0) write_char('-'), x = -x; static char tmp[16]; char* q = end(tmp); while (x >= 10000) memcpy(q -= 4, digits.data + x % 10000 * 4, 4), x /= 10000; if (x < 10) write_char('0' + x); else if (x < 100) write_char('0' + (uint8_t)x / 10), write_char('0' + (uint8_t)x % 10); else if (x < 1000) memcpy(p, digits.data + x * 4 + 1, 3), p += 3; else memcpy(p, digits.data + x * 4, 4), p += 4; memcpy(p, q, end(tmp) - q), p += end(tmp) - q; } template <class T> void_t<decltype(&T::val)> write(T x) { write(x.val()); } void write(double x) { static char tmp[40]; sprintf(tmp, "%.15f", x); write(tmp); } void write(long double x) { static char tmp[40]; sprintf(tmp, "%.15Lf", x); write(tmp); } void write(const char* s) { while (*s) *p++ = *s++; } void write(const string& s) { memcpy(p, s.c_str(), s.size()), p += s.size(); } template <class T, class U> void write(const pair<T, U>& x) { write(x.first), write_char(' '), write(x.second); } template <class... Ts> void write(const tuple<Ts...>& x) { write_tuple(x, make_index_sequence<sizeof...(Ts)>{}); } template <class... Ts> void write(const Ts&... xs) { ((write(xs), write_char(' ')), ...), --p; } template <class... Ts> void writeln(const Ts&... xs) { write(xs...), write_char('\n'); } template <class... Ts> void operator()(const Ts&... xs) { writeln(xs...); } template <class It> void iter(It first, It last, char sep = ' ') { if (first == last) write_char('\n'); else { while (first != last) write(*first++), write_char(sep); p[-1] = '\n'; } } template <class It> void iter1(It first, It last, char sep = ' ') { if (first == last) write_char('\n'); else { while (first != last) write(1 + *first++), write_char(sep); p[-1] = '\n'; } } template <class T> void vec(const vector<T>& v, char sep = ' ') { iter(all(v), sep); } template <class T> void write(const vector<T>& v) { vec(v), p--; } template <class T> void vec1(const vector<T>& v, char sep = ' ') { iter1(all(v), sep); } void del() { *--p = 0; } void Yes(bool b = true) { writeln(b ? "Yes" : "No"); } void YES(bool b = true) { writeln(b ? "YES" : "NO"); } void Takahashi(bool b = true) { writeln(b ? "Takahashi" : "Aoki"); } private: char buf[BufSize], *p = buf; template <class T, size_t... Is> void write_tuple(const T& x, index_sequence<Is...>) { ((write(get<Is>(x)), write_char(' ')), ...), --p; } struct four_digits { char data[40000]; constexpr four_digits() : data() { for (int i = 0; i < 10000; i++) for (int n = i, j = 4; j--;) data[i * 4 + j] = n % 10 + '0', n /= 10; } } static constexpr digits{}; public:
#define INSTANT(s) void s() { writeln(#s); }
  INSTANT(No) INSTANT(NO) INSTANT(Aoki) INSTANT(possible) INSTANT(Possible) INSTANT(POSSIBLE) INSTANT(impossible) INSTANT(Impossible) INSTANT(IMPOSSIBLE)
#undef INSTANT
};
stdin_reader<> in;
stdout_writer<> out;
#line 4 "mod/inv.hpp"
// #include <atcoder/modint>

template <class T = atcoder::modint998244353>
T inverse(int n) {
  static vector<T> v = {T(0), T(1)};
  while (v.size() <= n) {
    v.push_back(-v[T::mod() % v.size()] * (T::mod() / v.size()));
  }
  return v[n];
}
#line 3 "bit/ctz.hpp"

#pragma GCC target("bmi")

template <class T>
int ctz(T x) {
  if (!x) return sizeof(T) * 8;
  if constexpr (sizeof(T) <= sizeof(unsigned)) {
    return __builtin_ctz((unsigned)x);
  } else if constexpr (sizeof(T) <= sizeof(unsigned long long)) {
    return __builtin_ctzll((unsigned long long)x);
  } else if constexpr (sizeof(T) <= sizeof(unsigned long long) * 2) {
    unsigned long long y = x;
    return y ? ctz(y)
             : sizeof(y) * 8 + ctz((unsigned long long)(x >> sizeof(y) * 8));
  }
}
#line 3 "util/seed.hpp"

auto seed() {
#if defined(LOCAL) && !defined(NO_FIX_SEED)
  return 314169265258979;
#endif
  return chrono::steady_clock::now().time_since_epoch().count();
}
#line 3 "util/rand.hpp"

uint32_t rand32() {
  static uint32_t x = seed();
  x ^= x << 13;
  x ^= x >> 17;
  x ^= x << 5;
  return x;
}

uint64_t rand64() {
  return uint64_t(rand32()) << 32 | rand32();
}
#line 4 "mod/sqrt.hpp"

template <class T>
optional<T> mod_sqrt(T a) {
  // Tonelli-Shanks
  if (T::mod() <= 2) return a;
  if (a == T(0)) return T(0);
  if (a.pow((T::mod() - 1) / 2) == -1) return nullopt;
  int s = ctz(T::mod() - 1);
  int q = (T::mod() - 1) >> s;
  T x = a.pow((q + 1) / 2);
  T b = rand32();
  while (b.pow((T::mod() - 1) / 2) != -1) b = rand32();
  b = b.pow(q);
  T ia = a.inv();
  s -= 2;
  for (T e = ia * x * x; e != 1; b *= b, s--) {
    if (e.pow(1 << s) != 1) x *= b, e = ia * x * x;
  }
  return x;
}
#line 3 "arith/sat.hpp"

template <class T, class U>
auto sat_add(T a, U b) {
  using V = common_type_t<T, U>;
  V res;
  return __builtin_add_overflow((V)a, (V)b, &res)
             ? (a < 0 ? numeric_limits<V>::min() : numeric_limits<V>::max())
             : res;
}
template <class T, class U>
auto sat_sub(T a, U b) {
  using V = common_type_t<T, U>;
  V res;
  return __builtin_sub_overflow((V)a, (V)b, &res)
             ? (a < 0 ? numeric_limits<V>::min() : numeric_limits<V>::max())
             : res;
}
template <class T, class U>
auto sat_mul(T a, U b) {
  using V = common_type_t<T, U>;
  V res;
  return __builtin_mul_overflow((V)a, (V)b, &res)
             ? ((a < 0) == (b < 0) ? numeric_limits<V>::max()
                                   : numeric_limits<V>::min())
             : res;
}
#line 3 "types.hpp"

template <class It>
using val_t = typename iterator_traits<It>::value_type;
#line 4 "ps/fft.hpp"

#line 1 "atcoder/internal_bit.hpp"



#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
constexpr int bsf_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

}  // namespace internal

}  // namespace atcoder


#line 8 "ps/fft.hpp"

#ifndef ATCODER_CONVOLUTION_HPP
#define ATCODER_CONVOLUTION_HPP

namespace atcoder {

namespace internal {

template <
    class mint, int g = internal::primitive_root<mint::mod()>,
    internal::is_static_modint_t<mint>* = nullptr>
struct fft_info {
  static constexpr int rank2 = bsf_constexpr(mint::mod() - 1);
  mint root[rank2 + 1];   // root[i]^(2^i) == 1
  mint iroot[rank2 + 1];  // root[i] * iroot[i] == 1

  mint rate2[std::max(0, rank2 - 2 + 1)];
  mint irate2[std::max(0, rank2 - 2 + 1)];

  mint rate3[std::max(0, rank2 - 3 + 1)];
  mint irate3[std::max(0, rank2 - 3 + 1)];

  constexpr fft_info() : root(), iroot(), rate2(), irate2(), rate3(), irate3() {
    root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
    iroot[rank2] = root[rank2].inv();
    for (int i = rank2 - 1; i >= 0; i--) {
      root[i] = root[i + 1] * root[i + 1];
      iroot[i] = iroot[i + 1] * iroot[i + 1];
    }

    {
      mint prod = 1, iprod = 1;
      for (int i = 0; i <= rank2 - 2; i++) {
        rate2[i] = root[i + 2] * prod;
        irate2[i] = iroot[i + 2] * iprod;
        prod *= iroot[i + 2];
        iprod *= root[i + 2];
      }
    }
    {
      mint prod = 1, iprod = 1;
      for (int i = 0; i <= rank2 - 3; i++) {
        rate3[i] = root[i + 3] * prod;
        irate3[i] = iroot[i + 3] * iprod;
        prod *= iroot[i + 3];
        iprod *= root[i + 3];
      }
    }
  }
};

template <class It, internal::is_static_modint_t<val_t<It>>* = nullptr>
void butterfly(It a, It last) {
  using mint = val_t<It>;
  int n = last - a;
  int h = internal::ceil_pow2(n);

  static constexpr fft_info<mint> info;

  int len = 0;  // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
  while (len < h) {
    if (h - len == 1) {
      int p = 1 << (h - len - 1);
      mint rot = 1;
      for (int s = 0; s < (1 << len); s++) {
        int offset = s << (h - len);
        for (int i = 0; i < p; i++) {
          auto l = a[i + offset];
          auto r = a[i + offset + p] * rot;
          a[i + offset] = l + r;
          a[i + offset + p] = l - r;
        }
        if (s + 1 != (1 << len)) rot *= info.rate2[bsf(~(unsigned int)(s))];
      }
      len++;
    } else {
      // 4-base
      int p = 1 << (h - len - 2);
      mint rot = 1, imag = info.root[2];
      for (int s = 0; s < (1 << len); s++) {
        mint rot2 = rot * rot;
        mint rot3 = rot2 * rot;
        int offset = s << (h - len);
        for (int i = 0; i < p; i++) {
          auto mod2 = 1ULL * mint::mod() * mint::mod();
          auto a0 = 1ULL * a[i + offset].val();
          auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
          auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
          auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
          auto a1na3imag = 1ULL * mint(a1 + mod2 - a3).val() * imag.val();
          auto na2 = mod2 - a2;
          a[i + offset] = a0 + a2 + a1 + a3;
          a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
          a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
          a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
        }
        if (s + 1 != (1 << len)) rot *= info.rate3[bsf(~(unsigned int)(s))];
      }
      len += 2;
    }
  }
}

template <class mint>
void butterfly(std::vector<mint>& a) {
  butterfly(a.begin(), a.end());
}

template <class It, internal::is_static_modint_t<val_t<It>>* = nullptr>
void butterfly_inv(It a, It last) {
  using mint = val_t<It>;
  int n = last - a;
  int h = internal::ceil_pow2(n);

  static constexpr fft_info<mint> info;

  int len = h;  // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
  while (len) {
    if (len == 1) {
      int p = 1 << (h - len);
      mint irot = 1;
      for (int s = 0; s < (1 << (len - 1)); s++) {
        int offset = s << (h - len + 1);
        for (int i = 0; i < p; i++) {
          auto l = a[i + offset];
          auto r = a[i + offset + p];
          a[i + offset] = l + r;
          a[i + offset + p] =
              (unsigned long long)(mint::mod() + l.val() - r.val()) *
              irot.val();
        }
        if (s + 1 != (1 << (len - 1)))
          irot *= info.irate2[bsf(~(unsigned int)(s))];
      }
      len--;
    } else {
      // 4-base
      int p = 1 << (h - len);
      mint irot = 1, iimag = info.iroot[2];
      for (int s = 0; s < (1 << (len - 2)); s++) {
        mint irot2 = irot * irot;
        mint irot3 = irot2 * irot;
        int offset = s << (h - len + 2);
        for (int i = 0; i < p; i++) {
          auto a0 = 1ULL * a[i + offset + 0 * p].val();
          auto a1 = 1ULL * a[i + offset + 1 * p].val();
          auto a2 = 1ULL * a[i + offset + 2 * p].val();
          auto a3 = 1ULL * a[i + offset + 3 * p].val();

          auto a2na3iimag =
              1ULL * mint((mint::mod() + a2 - a3) * iimag.val()).val();

          a[i + offset] = a0 + a1 + a2 + a3;
          a[i + offset + 1 * p] =
              (a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
          a[i + offset + 2 * p] =
              (a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) * irot2.val();
          a[i + offset + 3 * p] =
              (a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *
              irot3.val();
        }
        if (s + 1 != (1 << (len - 2)))
          irot *= info.irate3[bsf(~(unsigned int)(s))];
      }
      len -= 2;
    }
  }
}

template <class mint>
void butterfly_inv(vector<mint>& a) {
  butterfly_inv(a.begin(), a.end());
}

template <class T>
std::vector<T> convolution_naive(
    const std::vector<T>& a, const std::vector<T>& b) {
  int n = int(a.size()), m = int(b.size());
  std::vector<T> ans(n + m - 1);
  if (n < m) {
    for (int j = 0; j < m; j++) {
      for (int i = 0; i < n; i++) {
        ans[i + j] += a[i] * b[j];
      }
    }
  } else {
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        ans[i + j] += a[i] * b[j];
      }
    }
  }
  return ans;
}

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
  int n = int(a.size()), m = int(b.size());
  int z = 1 << internal::ceil_pow2(n + m - 1);
  assert((mint::mod() - 1) % z == 0);
  a.resize(z);
  internal::butterfly(a);
  b.resize(z);
  internal::butterfly(b);
  for (int i = 0; i < z; i++) {
    a[i] *= b[i];
  }
  internal::butterfly_inv(a);
  a.resize(n + m - 1);
  mint iz = mint(z).inv();
  for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
  return a;
}

}  // namespace internal

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) {
  int n = int(a.size()), m = int(b.size());
  if (!n || !m) return {};
  if (std::min(n, m) <= 60) return convolution_naive(a, b);
  return internal::convolution_fft(a, b);
}

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(
    const std::vector<mint>& a, const std::vector<mint>& b) {
  int n = int(a.size()), m = int(b.size());
  if (!n || !m) return {};
  if (std::min(n, m) <= 60) return convolution_naive(a, b);
  return internal::convolution_fft(a, b);
}

template <
    unsigned int mod = 998244353, class T,
    std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
  int n = int(a.size()), m = int(b.size());
  if (!n || !m) return {};

  using mint = static_modint<mod>;
  std::vector<mint> a2(n), b2(m);
  for (int i = 0; i < n; i++) {
    a2[i] = mint(a[i]);
  }
  for (int i = 0; i < m; i++) {
    b2[i] = mint(b[i]);
  }
  auto c2 = convolution(move(a2), move(b2));
  std::vector<T> c(n + m - 1);
  for (int i = 0; i < n + m - 1; i++) {
    c[i] = c2[i].val();
  }
  return c;
}

template <class mint>
std::vector<mint> convolution_garner(
    const std::vector<mint>& a, const std::vector<mint>& b) {
  int n = int(a.size()), m = int(b.size());
  if (!n || !m) return {};
  if (std::min(n, m) <= 200) return internal::convolution_naive(a, b);

  static constexpr ll MOD = mint::mod();

  static constexpr ll MOD1 = 469762049;
  static constexpr ll MOD2 = 167772161;
  static constexpr ll MOD3 = 754974721;
  static constexpr ll MOD12 = MOD1 * MOD2 % MOD;

  static constexpr ll r12 = internal::inv_gcd(MOD1, MOD2).second;
  static constexpr ll r23 = internal::inv_gcd(MOD2, MOD3).second;
  static constexpr ll r123 = internal::inv_gcd(MOD1 * MOD2, MOD3).second;

  vector<int> ai(n), bi(m);
  rep(i, n) ai[i] = a[i].val();
  rep(i, m) bi[i] = b[i].val();
  auto c1 = convolution<MOD1>(ai, bi);
  auto c2 = convolution<MOD2>(ai, bi);
  auto c3 = convolution<MOD3>(ai, bi);

  std::vector<mint> c(n + m - 1);
  for (int i = 0; i < n + m - 1; i++) {
    long long x1 = c1[i];
    long long x2 = internal::safe_mod((c2[i] - x1) * r12, MOD2);
    long long x3 = internal::safe_mod((c3[i] - x1) * r123 - x2 * r23, MOD3);
    c[i] = x1 + x2 * MOD1 + x3 * MOD12;
  }

  return c;
}

std::vector<long long> convolution_ll(
    const std::vector<long long>& a, const std::vector<long long>& b) {
  int n = int(a.size()), m = int(b.size());
  if (!n || !m) return {};
  if (std::min(n, m) <= 200) return internal::convolution_naive(a, b);

  static constexpr unsigned long long MOD1 = 754974721;  // 2^24
  static constexpr unsigned long long MOD2 = 167772161;  // 2^25
  static constexpr unsigned long long MOD3 = 469762049;  // 2^26
  static constexpr unsigned long long M2M3 = MOD2 * MOD3;
  static constexpr unsigned long long M1M3 = MOD1 * MOD3;
  static constexpr unsigned long long M1M2 = MOD1 * MOD2;
  static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;

  static constexpr unsigned long long i1 =
      internal::inv_gcd(MOD2 * MOD3, MOD1).second;
  static constexpr unsigned long long i2 =
      internal::inv_gcd(MOD1 * MOD3, MOD2).second;
  static constexpr unsigned long long i3 =
      internal::inv_gcd(MOD1 * MOD2, MOD3).second;

  auto c1 = convolution<MOD1>(a, b);
  auto c2 = convolution<MOD2>(a, b);
  auto c3 = convolution<MOD3>(a, b);

  std::vector<long long> c(n + m - 1);
  for (int i = 0; i < n + m - 1; i++) {
    unsigned long long x = 0;
    x += (c1[i] * i1) % MOD1 * M2M3;
    x += (c2[i] * i2) % MOD2 * M1M3;
    x += (c3[i] * i3) % MOD3 * M1M2;
    // B = 2^63, -B <= x, r(real value) < B
    // (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
    // r = c1[i] (mod MOD1)
    // focus on MOD1
    // r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
    // r = x,
    //     x - M' + (0 or 2B),
    //     x - 2M' + (0, 2B or 4B),
    //     x - 3M' + (0, 2B, 4B or 6B) (without mod!)
    // (r - x) = 0, (0)
    //           - M' + (0 or 2B), (1)
    //           -2M' + (0 or 2B or 4B), (2)
    //           -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
    // we checked that
    //   ((1) mod MOD1) mod 5 = 2
    //   ((2) mod MOD1) mod 5 = 3
    //   ((3) mod MOD1) mod 5 = 4
    long long diff =
        c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
    if (diff < 0) diff += MOD1;
    static constexpr unsigned long long offset[5] = {
        0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
    x -= offset[diff % 5];
    c[i] = x;
  }

  return c;
}

}  // namespace atcoder

#endif  // ATCODER_CONVOLUTION_HPP

template <class It>
void fft(It a, It last) {
  atcoder::internal::butterfly(a, last);
}

template <class T>
void fft(vector<T>& a, int n = -1) {
  if (n != -1) a.resize(n);
  fft(all(a));
}

template <class It>
void ifft(It a, It last) {
  atcoder::internal::butterfly_inv(a, last);
}

template <class T>
void ifft(vector<T>& a) {
  ifft(all(a));
}

template <class T>
void double_fft(vector<T>& a) {
  static constexpr atcoder::internal::fft_info<T> info{};
  int m = a.size();
  a.resize(m * 2), copy(a.begin(), a.begin() + m, a.begin() + m);
  ifft(a.begin() + m, a.end());
  T z = T(m).inv();
  T w = info.root[ctz(m * 2)];
  rep2(i, m, m * 2) a[i] *= z, z *= w;
  fft(a.begin() + m, a.end());
}
#line 3 "ps/inv.hpp"

template <class T>
vector<T> inv(const vector<T>& f, int deg = -1) {
  assert(f[0] != 0);
  if (deg == -1) deg = f.size();
  int z = 1 << atcoder::internal::ceil_pow2(deg);
  vector<T> g = {1 / f[0]}, gfft(1);
  vector<T> h;
  g.reserve(z), gfft.reserve(z), h.reserve(z);
  const T i4 = T(4).inv();
  T imm4 = i4;
  for (int m = 1; m < z; m <<= 1, imm4 *= i4) {
    h.assign(f.begin(), f.begin() + min((int)f.size(), m * 2));
    copy(all(g), gfft.begin());
    fft(h, m * 2), fft(gfft, m * 2);
    rep(i, m * 2) h[i] *= gfft[i];
    ifft(h), fill(h.begin(), h.begin() + m, 0), fft(h);
    rep(i, m * 2) h[i] *= -gfft[i];
    ifft(h);
    rep2(i, m, m * 2) g.push_back(h[i] * imm4);
  }
  g.resize(deg);
  return g;
}
#line 8 "ps/fps.hpp"

template <class T>
vector<T> exp(const vector<T>& p, int deg = -1);
template <class T>
T bostan_mori(vector<T> a, vector<T> b, ll n);

template <
    class T,
    enable_if_t<is_base_of_v<atcoder::internal::modint_base, T>>* = nullptr>
class formal_power_series : public vector<T> {
 private:
  using fps = formal_power_series<T>;

 public:
  using sparse = vector<pair<int, T>>;

  using vector<T>::vector;
  formal_power_series(vector<T> v) : vector<T>(move(v)) { }
  formal_power_series(sparse p) : vector<T>() {
    this->resize(p.back().first + 1);
    for (auto [k, c] : p) (*this)[k] += c;
  }
  static fps one() { return fps({T(1)}); }
  static fps zero() { return fps{}; }

  int size() const { return vector<T>::size(); }
  const vector<T>& as_vec() const { return (const vector<T>&)*this; }
  vector<T>& as_vec() { return (vector<T>&)*this; }
  vector<T> into_vec() { return move(as_vec()); }
  T eval(T x) const {
    T pow(1), ans(0);
    for (auto e : *this) ans += e * pow, pow *= x;
    return ans;
  }
  void trunc() {
    while (!this->empty() && this->back() == T(0)) this->pop_back();
  }
  fps& operator*=(T c) {
    for (auto& e : *this) e *= c;
    return *this;
  }
  fps operator*(T c) && { return move(*this *= c); }
  fps operator*(T c) const& { return fps(*this) * c; }
  fps mul(T c) && { return move(*this) * c; }
  fps mul(T c) const& { return *this * c; }
  fps& operator+=(const fps& v) {
    this->resize(max(size(), v.size()));
    rep(i, v.size()) (*this)[i] += v[i];
    return *this;
  }
  fps operator+(const fps& v) && { return move(*this += v); }
  fps operator+(const fps& v) const& { return fps(*this) + v; }
  fps add(const fps& v) && { return move(*this += v); }
  fps add(const fps& v) const& { return fps(*this) + v; }
  fps& operator-=(const fps& v) {
    this->resize(max(size(), v.size()));
    rep(i, v.size()) (*this)[i] -= v[i];
    return *this;
  }
  fps operator-(const fps& v) && { return move(*this -= v); }
  fps operator-(const fps& v) const& { return fps(*this) - v; }
  fps sub(const fps& v) && { return move(*this -= v); }
  fps sub(const fps& v) const& { return fps(*this) - v; }
  fps conv(fps v, int deg = -1) && {
    if (~deg) this->resize(min(size(), deg)), v.resize(min(v.size(), deg));
    auto f = convolution(into_vec(), v.into_vec());
    if (~deg) f.resize(deg);
    return f;
  }
  fps conv(fps v, int deg = -1) const& { return fps(*this).conv(move(v), deg); }
  fps diff() && {
    rep(i, size() - 1) (*this)[i] = (*this)[i + 1] * (i + 1);
    this->pop_back();
    return move(*this);
  }
  fps diff() const& { return fps(*this).diff(); }
  fps integr() && {
    this->push_back(0);
    repr(i, size() - 1) (*this)[i + 1] = (*this)[i] * inverse(i + 1);
    (*this)[0] = 0;
    return move(*this);
  }
  fps integr() const& { return fps(*this).integr(); }
  fps inv(int deg = -1) const& { return fps(::inv(as_vec(), deg)); }
  fps div(const fps& v, int deg = -1) && {
    return move(*this).conv(v.inv(deg), deg);
  }
  fps div(const fps& v, int deg = -1) const& { return fps(*this).div(v, deg); }
  fps log(int deg = -1) && {
    return inv(deg - 1).conv(move(*this).diff(), deg - 1).integr();
  }
  fps log(int deg = -1) const& { return fps(*this).log(deg); }
  fps exp(int deg = -1) const& { return ::exp(as_vec(), deg); }
  fps pow(ll k, int deg = -1) && {
    if (deg == -1) deg = size();
    int z = -1;
    rep(i, size())
      if ((*this)[i] != 0) {
        z = i;
        break;
      }
    if (z == -1 || sat_mul<ll>(z, k) > deg) {
      fps res(deg, 0);
      res[0] = k == 0;
      return res;
    }
    ll rest = deg - z * k;
    this->erase(this->begin(), this->begin() + z);
    T c = (*this)[0].pow(k);
    fps f = move(*this).log(rest).mul(k).exp(rest);
    for (auto& e : f) e *= c;
    f.resize(deg);
    copy_backward(f.begin(), f.begin() + rest, f.end());
    fill(f.begin(), f.begin() + z * k, 0);
    return f;
  }
  fps pow(ll k, int deg = -1) const& { return fps(*this).pow(k, deg); }
  fps square(int deg = -1) && {
    if (deg == -1) deg = size() * 2 - 1;
    int n = 1 << atcoder::internal::ceil_pow2(deg);
    fft(as_vec(), n * 2);
    for (auto& e : *this) e *= e;
    ifft(as_vec());
    auto in2 = inverse(n * 2);
    this->resize(deg);
    for (auto& e : *this) e *= in2;
    return move(*this);
  }
  fps square(int deg = -1) const& { return fps(*this).square(deg); }
  T div_at(fps f, ll n) && { return bostan_mori(into_vec(), f.into_vec(), n); }
  T div_at(fps f, ll n) const& { return fps(*this).div_at(move(f), n); }
  optional<fps> sqrt(int deg = -1) && {
    if (deg == -1) deg = size();
    this->resize(deg);
    if (this->empty()) return move(*this);
    if ((*this)[0] == 0) {
      int b = 0;
      while (b < size() && (*this)[b] == 0) b++;
      if (b == size()) return move(*this);
      if (b % 2 != 0) return nullopt;
      this->erase(this->begin(), this->begin() + b);
      auto ans = move(*this).sqrt(deg - b / 2);
      if (ans) ans->insert(ans->begin(), b / 2, T(0));
      return ans;
    }
    auto x = mod_sqrt((*this)[0]);
    if (!x) return nullopt;
    fps f = {*x};
    int z = 1 << atcoder::internal::ceil_pow2(deg);
    f.reserve(z);
    const T i2 = inverse(2);
    for (int m = 1; m < z; m *= 2) {
      fps h(this->begin(), this->begin() + min(m * 2, size()));
      fps hf = move(h).div(f, m * 2);
      f = move(f).add(hf).mul(i2);
    }
    f.resize(deg);
    return f;
  }

  fps div_poly(fps g) && {
    int d = size() - g.size() + 1;
    if (d <= 0) return zero();
    reverse(all(*this));
    reverse(all(g));
    fps q = move(*this).div(move(g), d);
    reverse(all(q));
    return q;
  }
  fps div_poly(fps g) const& { return fps(*this).div_poly(move(g)); }
  pair<fps, fps> div_rem_poly(fps g) && {
    int d = g.size() - 1;
    fps q = div_poly(g);
    fps r = move(*this).sub(move(g).conv(q, d));
    r.resize(d);
    r.trunc();
    return pair(move(q), move(r));
  }
  pair<fps, fps> div_rem_poly(fps g) const& {
    return fps(*this).div_rem_poly(move(g));
  }

  fps conv(sparse v) && {
    if (v.empty()) return zero();
    if (v.front().first == 0) v.front().second -= T(1);
    repr(i, size())
      for (auto [k, c] : v) {
        if (k > i) break;
        (*this)[i] += (*this)[i - k] * c;
      }
    return move(*this);
  }
  fps conv(sparse v) const& { return fps(*this).conv(move(v)); }
  fps div(sparse v) && {
    auto [k0, r] = v.front();
    assert(k0 == 0 && r != T(0));
    T ir = r.inv();
    v.erase(v.begin());
    rep(i, size()) {
      for (auto [k, c] : v) {
        if (k > i) break;
        (*this)[i] -= (*this)[i - k] * c;
      }
      (*this)[i] *= ir;
    }
    return move(*this);
  }
  fps div(sparse v) const& { return fps(*this).div(move(v)); }

  template <class It>
  static fps prod(It first, It last) {
    if (first == last) return one();
    vector<fps> vec(first, last);
    vec.reserve(distance(first, last) * 2);
    for (int i = 0; i + 1 < vec.size(); i += 2)
      vec.push_back(move(vec[i]).conv(move(vec[i + 1])));
    return vec.back();
  }
};
#line 6 "test/ps/fps.log.test.cpp"
using mint = atcoder::modint998244353;
using fps = formal_power_series<mint>;

int main() {
  int n = in;
  fps f(in.vec<mint>(n));
  f = move(f).log(n);
  out.iter(all(f));
}

Test cases

Env Name Status Elapsed Memory
g++-12 example_00 :heavy_check_mark: AC 180 ms 11 MB
g++-12 max_all_zero_00 :heavy_check_mark: AC 650 ms 46 MB
g++-12 max_random_00 :heavy_check_mark: AC 656 ms 51 MB
g++-12 max_random_01 :heavy_check_mark: AC 657 ms 51 MB
g++-12 max_random_02 :heavy_check_mark: AC 658 ms 50 MB
g++-12 max_random_03 :heavy_check_mark: AC 657 ms 51 MB
g++-12 max_random_04 :heavy_check_mark: AC 658 ms 54 MB
g++-12 near_262144_00 :heavy_check_mark: AC 333 ms 32 MB
g++-12 near_262144_01 :heavy_check_mark: AC 332 ms 32 MB
g++-12 near_262144_02 :heavy_check_mark: AC 334 ms 34 MB
g++-12 random_00 :heavy_check_mark: AC 639 ms 49 MB
g++-12 random_01 :heavy_check_mark: AC 649 ms 49 MB
g++-12 random_02 :heavy_check_mark: AC 90 ms 16 MB
g++-12 random_03 :heavy_check_mark: AC 645 ms 48 MB
g++-12 random_04 :heavy_check_mark: AC 622 ms 42 MB
g++-12 small_degree_00 :heavy_check_mark: AC 24 ms 11 MB
g++-12 small_degree_01 :heavy_check_mark: AC 23 ms 11 MB
g++-12 small_degree_02 :heavy_check_mark: AC 23 ms 11 MB
g++-12 small_degree_03 :heavy_check_mark: AC 23 ms 11 MB
g++-12 small_degree_04 :heavy_check_mark: AC 23 ms 11 MB
g++-12 small_degree_05 :heavy_check_mark: AC 23 ms 11 MB
g++-12 small_degree_06 :heavy_check_mark: AC 24 ms 11 MB
g++-12 small_degree_07 :heavy_check_mark: AC 24 ms 11 MB
g++-12 small_degree_08 :heavy_check_mark: AC 24 ms 11 MB
g++-12 small_degree_09 :heavy_check_mark: AC 23 ms 11 MB
Back to top page