結果
| 問題 | No.3044 よくあるカエルさん |
| コンテスト | |
| ユーザー |
 zawakasu
|
| 提出日時 | 2026-01-03 20:56:37 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
AC
|
| 実行時間 | 3 ms / 2,000 ms |
| コード長 | 41,016 bytes |
| 記録 | |
| コンパイル時間 | 3,799 ms |
| コンパイル使用メモリ | 232,968 KB |
| 実行使用メモリ | 7,848 KB |
| 最終ジャッジ日時 | 2026-01-03 20:56:43 |
| 合計ジャッジ時間 | 5,269 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 20 |
ソースコード
#line 1 "3044.test.cpp"
// #define PROBLEM "https://yukicoder.me/problems/no/3044"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A"
#line 2 "/home/zawatin/compro/cp-documentation/Src/FPS/FPSNTTFriendly.hpp"
#line 2 "/home/zawatin/compro/cp-documentation/Src/FPS/FPS.hpp"
#line 2 "/home/zawatin/compro/cp-documentation/Src/Template/TypeAlias.hpp"
#include <cstdint>
#include <cstddef>
namespace zawa {
using i16 = std::int16_t;
using i32 = std::int32_t;
using i64 = std::int64_t;
using i128 = __int128_t;
using u8 = std::uint8_t;
using u16 = std::uint16_t;
using u32 = std::uint32_t;
using u64 = std::uint64_t;
using usize = std::size_t;
} // namespace zawa
#line 4 "/home/zawatin/compro/cp-documentation/Src/FPS/FPS.hpp"
#include <concepts>
namespace zawa {
namespace concepts {
template <class FPS>
concept IndexedFPS = requires(FPS f, usize i) {
typename FPS::value_type;
{ f.size() } -> std::convertible_to<usize>;
{ f[i] } -> std::convertible_to<typename FPS::value_type>;
f.reserve(0);
f.push_back(f[i]);
};
template <class FPS, class Conv>
concept Convolution =
std::regular_invocable<Conv, const FPS&, const FPS&> &&
std::same_as<std::invoke_result_t<Conv, const FPS&, const FPS&>, FPS>;
} // namespace concepts
struct FPSMult {
template <class FPS>
requires requires(const FPS& a, const FPS& b) {
{ a * b } -> std::same_as<FPS>;
}
FPS operator()(const FPS& a, const FPS& b) const {
return a * b;
}
};
struct NaiveConvolution {
template <class FPS>
FPS operator()(const FPS& a, const FPS& b) const {
if (a.empty())
return b;
if (b.empty())
return a;
FPS res(a.size() + b.size() - 1);
for (usize i = 0 ; i < a.size() ; i++)
for (usize j = 0 ; j < b.size() ; j++)
res[i + j] += a[i] * b[j];
return res;
}
};
} // namespace zawa
#line 5 "/home/zawatin/compro/cp-documentation/Src/FPS/FPSNTTFriendly.hpp"
#line 1 "/home/zawatin/compro/ac-library/atcoder/modint.hpp"
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#line 1 "/home/zawatin/compro/ac-library/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`
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 long long y = x * _m;
return (unsigned int)(z - y + (z < y ? _m : 0));
}
};
// @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 "/home/zawatin/compro/ac-library/atcoder/internal_type_traits.hpp"
#line 7 "/home/zawatin/compro/ac-library/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 "/home/zawatin/compro/ac-library/atcoder/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 mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T 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>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
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 -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
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 {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
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;
}
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());
}
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;
}
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 1 "/home/zawatin/compro/ac-library/atcoder/convolution.hpp"
#include <algorithm>
#include <array>
#line 8 "/home/zawatin/compro/ac-library/atcoder/convolution.hpp"
#include <vector>
#line 1 "/home/zawatin/compro/ac-library/atcoder/internal_bit.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
#if __cplusplus >= 202002L
#include <bit>
#endif
namespace atcoder {
namespace internal {
#if __cplusplus >= 202002L
using std::bit_ceil;
#else
// @return same with std::bit::bit_ceil
unsigned int bit_ceil(unsigned int n) {
unsigned int x = 1;
while (x < (unsigned int)(n)) x *= 2;
return x;
}
#endif
// @param n `1 <= n`
// @return same with std::bit::countr_zero
int countr_zero(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
// @param n `1 <= n`
// @return same with std::bit::countr_zero
constexpr int countr_zero_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
} // namespace internal
} // namespace atcoder
#line 12 "/home/zawatin/compro/ac-library/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 = countr_zero_constexpr(mint::mod() - 1);
std::array<mint, rank2 + 1> root; // root[i]^(2^i) == 1
std::array<mint, rank2 + 1> iroot; // root[i] * iroot[i] == 1
std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;
std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;
fft_info() {
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 mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
int n = int(a.size());
int h = internal::countr_zero((unsigned int)n);
static const 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[countr_zero(~(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[countr_zero(~(unsigned int)(s))];
}
len += 2;
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
int n = int(a.size());
int h = internal::countr_zero((unsigned int)n);
static const 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)((unsigned int)(l.val() - r.val()) + mint::mod()) *
irot.val();
;
}
if (s + 1 != (1 << (len - 1)))
irot *= info.irate2[countr_zero(~(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[countr_zero(~(unsigned int)(s))];
}
len -= 2;
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_naive(const std::vector<mint>& a,
const std::vector<mint>& b) {
int n = int(a.size()), m = int(b.size());
std::vector<mint> 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 = (int)internal::bit_ceil((unsigned int)(n + m - 1));
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 {};
int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
assert((mint::mod() - 1) % z == 0);
if (std::min(n, m) <= 60) return convolution_naive(std::move(a), std::move(b));
return internal::convolution_fft(std::move(a), std::move(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 {};
int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
assert((mint::mod() - 1) % z == 0);
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>;
int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
assert((mint::mod() - 1) % z == 0);
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(std::move(a2), std::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;
}
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 {};
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;
static constexpr int MAX_AB_BIT = 24;
static_assert(MOD1 % (1ull << MAX_AB_BIT) == 1, "MOD1 isn't enough to support an array length of 2^24.");
static_assert(MOD2 % (1ull << MAX_AB_BIT) == 1, "MOD2 isn't enough to support an array length of 2^24.");
static_assert(MOD3 % (1ull << MAX_AB_BIT) == 1, "MOD3 isn't enough to support an array length of 2^24.");
assert(n + m - 1 <= (1 << MAX_AB_BIT));
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
#line 8 "/home/zawatin/compro/cp-documentation/Src/FPS/FPSNTTFriendly.hpp"
#line 10 "/home/zawatin/compro/cp-documentation/Src/FPS/FPSNTTFriendly.hpp"
#include <iostream>
#include <ranges>
#line 14 "/home/zawatin/compro/cp-documentation/Src/FPS/FPSNTTFriendly.hpp"
namespace zawa {
template <usize MOD = 998244353>
struct FPSNTTFriendly : public std::vector<atcoder::static_modint<MOD>> {
using std::vector<atcoder::static_modint<MOD>>::vector;
using V = atcoder::static_modint<MOD>;
FPSNTTFriendly(const std::vector<V>& f) {
this->reserve(f.size());
for (V v : f) this->push_back(std::move(v));
}
[[nodiscard]] FPSNTTFriendly<MOD> resized(usize n) const {
auto cp = *this;
cp.resize(n);
return cp;
}
[[nodiscard]] FPSNTTFriendly<MOD> inv(usize n) const {
assert(this->size() and (*this)[0] != V{0});
FPSNTTFriendly<MOD> g{this->front().inv()};
while (g.size() < n) {
auto fgg = [&]() {
auto res = g;
FPSNTTFriendly<MOD> f(resized(g.size() << 1));
const usize m = res.size(), k = f.size(), s = (m + m - 1) + k - 1;
const usize z = atcoder::internal::bit_ceil(s);
res.resize(z);
f.resize(z);
atcoder::internal::butterfly(res);
atcoder::internal::butterfly(f);
for (usize i = 0 ; i < z ; i++) res[i] *= res[i] * f[i];
atcoder::internal::butterfly_inv(res);
res.resize(k);
res *= V{z}.inv();
return res;
}();
// auto gg = atcoder::convolution(g, g);
// std::vector<T> f(g.size() << 1);
// for (usize i = 0 ; i < std::min(f.size(), F.size()) ; i++) f[i] = F[i];
// auto fgg = atcoder::convolution(f, gg);
g = V{2} * g - fgg;
}
g.resize(n);
return g;
}
[[nodiscard]] FPSNTTFriendly<MOD> inv() const {
return inv(this->size());
}
[[nodiscard]] FPSNTTFriendly<MOD> differential() const {
if (this->empty()) return FPSNTTFriendly{};
FPSNTTFriendly res(this->size() - 1);
for (usize i = 1 ; i < this->size() ; i++) {
res[i - 1] = (*this)[i] * V{i};
}
return res;
}
// C = 0
[[nodiscard]] FPSNTTFriendly<MOD> integral() const {
FPSNTTFriendly<MOD> res(this->size() + 1);
for (usize i = 0 ; i < this->size() ; i++) {
res[i + 1] = (*this)[i] / V{i + 1};
}
return res;
}
[[nodiscard]] FPSNTTFriendly<MOD> log(usize n) const {
assert(this->size() and (*this)[0] == V{1});
return FPSNTTFriendly<MOD>{differential() / (*this)}.resized(n - 1).integral();
}
[[nodiscard]] FPSNTTFriendly<MOD> log() const {
return log(this->size());
}
[[nodiscard]] FPSNTTFriendly<MOD> exp(usize n) const {
assert(this->size() and (*this)[0] == 0);
FPSNTTFriendly<MOD> g{V{1}};
for (usize sz = 1 ; sz < n ; sz <<= 1) {
auto f = -g.resized(sz << 1).log() + (*this).resized(sz << 1);
f[0] += 1;
g = g * f;
g.resize(sz << 1);
}
g.resize(n);
return g;
}
[[nodiscard]] FPSNTTFriendly<MOD> exp() const {
return exp(this->size());
}
[[nodiscard]] FPSNTTFriendly<MOD> pow(u64 k, usize n) const {
if (k == 0) return FPSNTTFriendly<MOD>{V{1}}.resized(n);
auto it = std::ranges::find_if(*this, [&](const auto& v) { return v != V{0}; });
if (it == this->end()) return FPSNTTFriendly<MOD>(n);
auto sh = it - this->begin();
if (sh and k > n / sh) return FPSNTTFriendly<MOD>(n);
FPSNTTFriendly<MOD> f(this->size() - sh);
const auto pv = it->pow(k);
const auto iv = it->inv();
for (usize i = 0 ; i < f.size() ; i++) f[i] = (*this)[sh + i] * iv;
f = (f.log(n) * V{k}).exp(n);
FPSNTTFriendly<MOD> res(n);
for (usize i = 0 ; i + sh * k < n ; i++) res[i + sh * k] = f[i] * pv;
return res;
}
[[nodiscard]] FPSNTTFriendly<MOD> pow(u64 k) const {
return pow(k, this->size());
}
FPSNTTFriendly<MOD> operator+() const {
return *this;
}
FPSNTTFriendly<MOD> operator-() const {
FPSNTTFriendly<MOD> f = *this;
for (usize i = 0 ; i < this->size() ; i++) f[i] *= V::raw(MOD - 1);
return f;
}
FPSNTTFriendly<MOD>& operator+=(const FPSNTTFriendly<MOD>& f) {
if (this->size() < f.size()) this->resize(f.size());
for (usize i = 0 ; i < f.size() ; i++) (*this)[i] += f[i];
return *this;
}
FPSNTTFriendly<MOD>& operator-=(const FPSNTTFriendly<MOD>& f) {
if (this->size() < f.size()) this->resize(f.size());
for (usize i = 0 ; i < f.size() ; i++) (*this)[i] -= f[i];
return *this;
}
FPSNTTFriendly<MOD>& operator*=(const V& v) {
for (usize i = 0 ; i < this->size() ; i++) (*this)[i] *= v;
return *this;
}
friend FPSNTTFriendly<MOD> operator*(const FPSNTTFriendly<MOD>& l, const atcoder::static_modint<MOD>& r) {
return FPSNTTFriendly<MOD>{l} *= r;
}
friend FPSNTTFriendly<MOD> operator*(const atcoder::static_modint<MOD>& l, const FPSNTTFriendly<MOD>& r) {
return FPSNTTFriendly<MOD>{r} *= l;
}
FPSNTTFriendly<MOD>& operator*=(FPSNTTFriendly<MOD> f) {
auto l = *this;
auto r = std::move(f);
auto conved = atcoder::convolution(l, r);
return *this = std::move(conved);
}
FPSNTTFriendly<MOD>& operator/=(const V& v) {
return (*this) *= v.inv();
}
friend FPSNTTFriendly<MOD> operator/(const FPSNTTFriendly<MOD>& l, const atcoder::static_modint<MOD>& r) {
return FPSNTTFriendly<MOD>{l} /= r;
}
FPSNTTFriendly<MOD>& operator/=(FPSNTTFriendly<MOD> f) {
return (*this) *= f.inv();
}
};
template <usize MOD = 998244353>
FPSNTTFriendly<MOD> operator+(const FPSNTTFriendly<MOD>& l, const FPSNTTFriendly<MOD>& r) {
return FPSNTTFriendly<MOD>{l} += r;
}
template <usize MOD = 998244353>
FPSNTTFriendly<MOD> operator-(const FPSNTTFriendly<MOD>& l, const FPSNTTFriendly<MOD>& r) {
return FPSNTTFriendly<MOD>{l} -= r;
}
template <usize MOD = 998244353>
FPSNTTFriendly<MOD> operator*(const FPSNTTFriendly<MOD>& l, const FPSNTTFriendly<MOD>& r) {
return atcoder::convolution(l, r);
}
template <usize MOD = 998244353>
FPSNTTFriendly<MOD> operator/(const FPSNTTFriendly<MOD>& l, const FPSNTTFriendly<MOD>& r) {
return FPSNTTFriendly<MOD>{atcoder::convolution(l, r.inv())};
}
template <usize MOD = 998244353>
std::ostream& operator<<(std::ostream& os, const FPSNTTFriendly<MOD>& f) {
for (usize i = 0 ; i < f.size() ; i++) os << f[i].val() << (i + 1 == f.size() ? "" : " ");
return os;
}
template <usize MOD = 998244353>
std::istream& operator>>(std::istream& is, FPSNTTFriendly<MOD>& f) {
for (auto& v : f) {
i64 x;
is >> x;
v = atcoder::static_modint<MOD>{x};
}
return is;
}
template <usize MOD = 998244353>
using FPS = FPSNTTFriendly<MOD>;
} // namespace zawa
#line 2 "/home/zawatin/compro/cp-documentation/Src/FPS/KthTerm.hpp"
#line 5 "/home/zawatin/compro/cp-documentation/Src/FPS/KthTerm.hpp"
#line 2 "/home/zawatin/compro/cp-documentation/Src/FPS/BostanMori.hpp"
#line 4 "/home/zawatin/compro/cp-documentation/Src/FPS/BostanMori.hpp"
namespace zawa {
template <concepts::IndexedFPS FPS, class Conv = FPSMult>
requires concepts::Convolution<FPS, Conv>
typename FPS::value_type BostanMori(usize N, FPS P, FPS Q, Conv conv = {}) {
assert(P.size());
assert(Q.size() and Q[0] != 0);
auto takeParity = [&](const FPS& f, usize p) {
FPS res;
res.reserve(f.size() / 2);
for (usize i = p ; i < f.size() ; i += 2)
res.push_back(f[i]);
return res;
};
while (N) {
FPS Qm(Q.size());
for (usize i = 0 ; i < Q.size() ; i++)
Qm[i] = i % 2 ? -Q[i] : Q[i];
P = takeParity(conv(P, Qm), N % 2);
Q = takeParity(conv(Q, Qm), 0);
N >>= 1;
}
return P[0] / Q[0];
}
} // namespace zawa
#line 8 "/home/zawatin/compro/cp-documentation/Src/FPS/KthTerm.hpp"
namespace zawa {
template <concepts::IndexedFPS FPS, class Conv = FPSMult>
typename FPS::value_type KthTerm(u64 K, FPS A, FPS C, Conv conv = {}) {
assert(C.size() >= 2 and C[0] == 0);
assert(A.size() >= C.size() - 1);
if (K < A.size())
return A[K];
for (auto& v : C)
v = -v;
C[0] = 1;
FPS multed = conv(A, C);
multed.resize(C.size() - 1);
return BostanMori(K, multed, C, conv);
}
} // namespace zawa
#line 6 "3044.test.cpp"
/*
* yukicoder No. 3044 繧医￥縺ゅｋ繧ｫ繧ｨ繝ｫ縺輔ｓ
* https://yukicoder.me/submissions/1142529
*/
#line 14 "3044.test.cpp"
#line 16 "3044.test.cpp"
using namespace zawa;
using mint = atcoder::modint998244353;
using fps = FPSNTTFriendly<mint::mod()>;
void solve() {
int N, T, k, l;
std::cin >> N >> T >> k >> l;
fps C(T + 1);
C[1] = mint::raw(k - 1) / mint::raw(6);
C[2] = mint::raw(l - k) / mint::raw(6);
C[T] = mint::raw(7 - l) / mint::raw(6);
fps A(T);
A[0] = 1;
for (int n = 1 ; n < T ; n++) {
for (int j = 1 ; j <= T and n - j >= 0 ; j++) {
A[n] += C[j] * A[n - j];
}
}
std::cout << KthTerm(N - 1, A, C).val() << '\n';
}
int main() {
#ifdef ONLINE_JUDGE
solve();
#else
std::cout << "Hello World\n";
#endif
}