結果
問題 | No.2670 Sum of Products of Interval Lengths |
ユーザー | nok0 |
提出日時 | 2024-03-08 23:06:25 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 53 ms / 2,000 ms |
コード長 | 60,614 bytes |
コンパイル時間 | 3,593 ms |
コンパイル使用メモリ | 257,400 KB |
実行使用メモリ | 9,884 KB |
最終ジャッジ日時 | 2024-09-29 20:35:33 |
合計ジャッジ時間 | 4,829 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge1 |
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ファイルパターン | 結果 |
---|---|
other | AC * 17 |
ソースコード
#line 2 "/home/nok0/documents/programming/library/math/fps.hpp"#include <iostream>#include <random>#line 1 "/home/nok0/documents/programming/library/atcoder/convolution.hpp"#include <algorithm>#include <array>#include <cassert>#include <type_traits>#include <vector>#line 1 "/home/nok0/documents/programming/library/atcoder/internal_bit.hpp"#ifdef _MSC_VER#include <intrin.h>#endifnamespace 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_VERunsigned long index;_BitScanForward(&index, n);return index;#elsereturn __builtin_ctz(n);#endif}} // namespace internal} // namespace atcoder#line 1 "/home/nok0/documents/programming/library/atcoder/modint.hpp"#line 5 "/home/nok0/documents/programming/library/atcoder/modint.hpp"#include <numeric>#line 7 "/home/nok0/documents/programming/library/atcoder/modint.hpp"#ifdef _MSC_VER#include <intrin.h>#endif#line 1 "/home/nok0/documents/programming/library/atcoder/internal_math.hpp"#include <utility>#ifdef _MSC_VER#include <intrin.h>#endifnamespace atcoder {namespace internal {// @param m `1 <= m`// @return x mod mconstexpr 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 Lakestruct 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 munsigned 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 + 1unsigned long long z = a;z *= b;#ifdef _MSC_VERunsigned long long x;_umul128(z, im, &x);#elseunsigned long long x =(unsigned long long)(((unsigned __int128)(z)*im) >> 64);#endifunsigned 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/gconstexpr 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| <= blong 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| <= bauto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}// by [3]: |m0| <= b/g// by g != b: |m0| < b/gif (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) <= nn = (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/nok0/documents/programming/library/atcoder/internal_type_traits.hpp"#line 7 "/home/nok0/documents/programming/library/atcoder/internal_type_traits.hpp"namespace atcoder {namespace internal {#ifndef _MSC_VERtemplate <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;#elsetemplate <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;#endiftemplate <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/nok0/documents/programming/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 internaltemplate <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());}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 -= 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());}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;}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 12 "/home/nok0/documents/programming/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 = bsf_constexpr(mint::mod() - 1);std::array<mint, rank2 + 1> root; // root[i]^(2^i) == 1std::array<mint, rank2 + 1> iroot; // root[i] * iroot[i] == 1std::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::ceil_pow2(n);static const fft_info<mint> info;int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformedwhile (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-baseint 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, internal::is_static_modint_t<mint>* = nullptr>void butterfly_inv(std::vector<mint>& a) {int n = int(a.size());int h = internal::ceil_pow2(n);static const fft_info<mint> info;int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformedwhile (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-baseint 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, 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 = 1 << internal::ceil_pow2(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 internaltemplate <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;}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; // 2^24static constexpr unsigned long long MOD2 = 167772161; // 2^25static constexpr unsigned long long MOD3 = 469762049; // 2^26static 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 = 4long 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 4 "/home/nok0/documents/programming/library/math/factorial.hpp"template <class T>struct factorial {private:int _n;std::vector<T> _fac, _inv, _finv;void extend(int n) {n++;if(n <= _n) return;_fac.resize(n);_inv.resize(n);_finv.resize(n);for(int i = _n; i < n; i++) {_fac[i] = _fac[i - 1] * i;_inv[i] = (-_inv[T::mod() % i]) * (T::mod() / i);_finv[i] = _finv[i - 1] * _inv[i];}_n = n;}public:explicit factorial(int n = 2) {_n = 2;_fac = {1, 1};_inv = {1, 1};_finv = {1, 1};extend(n);}T fac(int k) {if(k < 0) return 0;extend(k);return _fac[k];}T inv(int k) {extend(k);return _inv[k];}T finv(int k) {extend(k);return _finv[k];}T binom(int n, int k) {if(k < 0 or n < k) return 0;extend(n);return _fac[n] * _finv[k] * _finv[n - k];}T large_binom(long long n, int k) {if(k < 0 or n < k) return 0;extend(k);T ret = _finv[k];for(int i = n; i > n - k; i--) ret *= i;return ret;}T catalan(int n) {extend(n * 2);return binom(n * 2, n) * _inv[n + 1];}T perm(int n, int k) {if(k < 0 or n < k) return 0;extend(n);return _fac[n] * _finv[n - k];}};#line 8 "/home/nok0/documents/programming/library/math/fps.hpp"enum Mode {FAST = 1,NAIVE = -1,};template <class T, Mode mode = FAST>struct formal_power_series : std::vector<T> {using std::vector<T>::vector;using std::vector<T>::size;using std::vector<T>::resize;using std::vector<T>::begin;using std::vector<T>::insert;using std::vector<T>::erase;using F = formal_power_series;using S = std::vector<std::pair<int, T>>;F &operator+=(const F &g) {for(int i = 0; i < int(std::min((*this).size(), g.size())); i++) (*this)[i] += g[i];return *this;}F &operator+=(const T &t) {assert(int((*this).size()));(*this)[0] += t;return *this;}F &operator-=(const F &g) {for(int i = 0; i < int(std::min((*this).size(), g.size())); i++) (*this)[i] -= g[i];return *this;}F &operator-=(const T &t) {assert(int((*this).size()));(*this)[0] -= t;return *this;}F &operator*=(const T &t) {for(int i = 0; i < int((*this).size()); ++i) (*this)[i] *= t;return *this;}F &operator/=(const T &t) {T div = t.inv();for(int i = 0; i < int((*this).size()); ++i) (*this)[i] *= div;return *this;}F &operator>>=(const int sz) {assert(sz >= 0);int n = (*this).size();(*this).erase((*this).begin(), (*this).begin() + std::min(sz, n));(*this).resize(n);return *this;}F &operator<<=(const int sz) {assert(sz >= 0);int n = (*this).size();(*this).insert((*this).begin(), sz, T(0));(*this).resize(n);return *this;}F poly_div(const F &g) {if(this->size() < g.size()) {F ret(this->size());return ret;}if(mode == FAST) {auto ret = *this;int old = this->size();int n = old - g.size() + 1;ret = ((*this).rev().pre(n) * g.rev().inv(n));ret.rev_inplace();ret.resize(old);return ret;} else {assert(g.back() != T(0));T igb = g.back().inv();int n = (*this).size(), m = g.size();F this_copy(*this);F ret(n);for(int i = n - 1; i >= m - 1; --i) {T mul = this_copy[i] * igb;ret[i - m + 1] = mul;for(int j = i; j > i - m; j--)this_copy[j] -= g[j - i + m - 1] * mul;}return ret;}}// これのみ多項式の除算として扱うF &operator%=(const F &g) {return *this -= this->poly_div(g) * g;}F &operator=(const std::vector<T> &v) {int n = (*this).size();for(int i = 0; i < n; ++i) (*this)[i] = v[i];return *this;}F operator-() const {F ret = *this;return ret * -1;}F &operator*=(const F &g) {if(mode == FAST) {int n = (*this).size();auto tmp = atcoder::convolution(*this, g);for(int i = 0; i < n; ++i) (*this)[i] = tmp[i];return *this;} else {int n = (*this).size(), m = g.size();for(int i = n - 1; i >= 0; --i) {(*this)[i] *= g[0];for(int j = 1; j < std::min(i + 1, m); j++)(*this)[i] += (*this)[i - j] * g[j];}return *this;}}F &operator/=(const F &g) {if((*this).size() < g.size()) {(*this).assign((*this).size(), T(0));return *this;}if(mode == FAST) {*this *= g.inv();return *this;} else {assert(g[0] != T(0));T ig0 = g[0].inv();int n = (*this).size(), m = g.size();for(int i = 0; i < n; ++i) {for(int j = 1; j < std::min(i + 1, m); ++j)(*this)[i] -= (*this)[i - j] * g[j];(*this)[i] *= ig0;}return *this;}}F &operator*=(S g) {int n = (*this).size();auto [d, c] = g.front();if(!d)g.erase(g.begin());elsec = 0;for(int i = n - 1; i >= 0; --i) {(*this)[i] *= c;for(auto &[j, b] : g) {if(j > i) break;(*this)[i] += (*this)[i - j] * b;}}return *this;}F &operator/=(S g) {int n = (*this).size();auto [d, c] = g.front();assert(!d and c != 0);T ic = c.inv();g.erase(g.begin());for(int i = 0; i < n; ++i) {for(auto &[j, b] : g) {if(j > i) break;(*this)[i] -= (*this)[i - j] * b;}(*this)[i] *= ic;}return *this;}F operator+(const F &g) const { return F(*this) += g; }F operator+(const T &t) const { return F(*this) += t; }F operator-(const F &g) const { return F(*this) -= g; }F operator-(const T &t) const { return F(*this) -= t; }F operator*(const F &g) const { return F(*this) *= g; }F operator*(const T &t) const { return F(*this) *= t; }F operator/(const F &g) const { return F(*this) /= g; }F operator/(const T &t) const { return F(*this) /= t; }F operator%(const F &g) const { return F(*this) %= g; }F operator*=(const S &g) const { return F(*this) *= g; }F operator/=(const S &g) const { return F(*this) /= g; }F operator<<(const int sz) const { return F(*this) <<= sz; }F operator>>(const int sz) const { return F(*this) >>= sz; }F pre(int d) const { return F((*this).begin(), (*this).begin() + std::min((int)(*this).size(), d)); }F &shrink() {while(!(*this).empty() and (*this).back() == T(0)) (*this).pop_back();return *this;}F &rev_inplace() {reverse((*this).begin(), (*this).end());return *this;}F rev() const { return F(*this).rev_inplace(); }// *=(1 + cz^d)F &multiply(const int d, const T c) {int n = (*this).size();if(c == T(1))for(int i = n - d - 1; i >= 0; --i)(*this)[i + d] += (*this)[i];else if(c == T(-1))for(int i = n - d - 1; i >= 0; --i)(*this)[i + d] -= (*this)[i];elsefor(int i = n - d - 1; i >= 0; --i)(*this)[i + d] += (*this)[i] * c;return *this;}// /=(1 + cz^d)F ÷(const int d, const T c) {int n = (*this).size();if(c == T(1))for(int i = 0; i < n - d; ++i) (*this)[i + d] -= (*this)[i];else if(c == T(-1))for(int i = 0; i < n - d; ++i) (*this)[i + d] += (*this)[i];elsefor(int i = 0; i < n - d; ++i) (*this)[i + d] -= (*this)[i] * c;return *this;}// Ο(N)T eval(const T &t) const {int n = (*this).size();T res = 0, tmp = 1;for(int i = 0; i < n; ++i) res += (*this)[i] * tmp, tmp *= t;return res;}F inv(int deg = -1) const {int n = (*this).size();assert(mode == FAST and n and (*this)[0] != 0);if(deg == -1) deg = n;assert(deg > 0);F res{(*this)[0].inv()};while(int(res.size()) < deg) {int m = res.size();F f((*this).begin(), (*this).begin() + std::min(n, m * 2)), r(res);f.resize(m * 2), atcoder::internal::butterfly(f);r.resize(m * 2), atcoder::internal::butterfly(r);for(int i = 0; i < m * 2; ++i) f[i] *= r[i];atcoder::internal::butterfly_inv(f);f.erase(f.begin(), f.begin() + m);f.resize(m * 2), atcoder::internal::butterfly(f);for(int i = 0; i < m * 2; ++i) f[i] *= r[i];atcoder::internal::butterfly_inv(f);T iz = T(m * 2).inv();iz *= -iz;for(int i = 0; i < m; ++i) f[i] *= iz;res.insert(res.end(), f.begin(), f.begin() + m);}res.resize(deg);return res;}// Ο(N)F &diff_inplace() {int n = (*this).size();for(int i = 1; i < n; ++i) (*this)[i - 1] = (*this)[i] * i;(*this)[n - 1] = 0;return *this;}F diff() const { return F(*this).diff_inplace(); }// Ο(N)F &integral_inplace() {int n = (*this).size(), mod = T::mod();std::vector<T> inv(n);{inv[1] = 1;for(int i = 2; i < n; ++i)inv[i] = T(mod) - inv[mod % i] * (mod / i);}for(int i = n - 2; i >= 0; --i) (*this)[i + 1] = (*this)[i] * inv[i + 1];(*this)[0] = 0;return *this;}F integral() const { return F(*this).integral_inplace(); }// Ο(NlogN)F &log_inplace() {int n = (*this).size();assert(n and (*this)[0] == 1);F f_inv = (*this).inv();(*this).diff_inplace();(*this) *= f_inv;(*this).integral_inplace();return *this;}F log() const { return F(*this).log_inplace(); }// Ο(NlogN)F &deriv_inplace() {int n = (*this).size();assert(n);for(int i = 2; i < n; ++i) (*this)[i] *= i;(*this).erase((*this).begin());(*this).push_back(0);return *this;}F deriv() const { return F(*this).deriv_inplace(); }// Ο(NlogN)F &exp_inplace() {int n = (*this).size();assert(n and (*this)[0] == 0);F g{1};(*this)[0] = 1;F h_drv((*this).deriv());for(int m = 1; m < n; m *= 2) {F f((*this).begin(), (*this).begin() + m);f.resize(2 * m), atcoder::internal::butterfly(f);auto mult_f = [&](F &p) {p.resize(2 * m);atcoder::internal::butterfly(p);for(int i = 0; i < 2 * m; ++i) p[i] *= f[i];atcoder::internal::butterfly_inv(p);p /= 2 * m;};if(m > 1) {F g_(g);g_.resize(2 * m), atcoder::internal::butterfly(g_);for(int i = 0; i < 2 * m; ++i) g_[i] *= g_[i] * f[i];atcoder::internal::butterfly_inv(g_);T iz = T(-2 * m).inv();g_ *= iz;g.insert(g.end(), g_.begin() + m / 2, g_.begin() + m);}F t((*this).begin(), (*this).begin() + m);t.deriv_inplace();{F r{h_drv.begin(), h_drv.begin() + m - 1};mult_f(r);for(int i = 0; i < m; ++i) t[i] -= r[i] + r[m + i];}t.insert(t.begin(), t.back());t.pop_back();t *= g;F v((*this).begin() + m, (*this).begin() + std::min(n, 2 * m));v.resize(m);t.insert(t.begin(), m - 1, 0);t.push_back(0);t.integral_inplace();for(int i = 0; i < m; ++i) v[i] -= t[m + i];mult_f(v);for(int i = 0; i < std::min(n - m, m); ++i)(*this)[m + i] = v[i];}return *this;}F exp() const { return F(*this).exp_inplace(); }// Ο(NlogN)F &pow_inplace(long long k) {int n = (*this).size(), l = 0;assert(k >= 0);if(!k) {for(int i = 0; i < n; ++i) (*this)[i] = !i;return *this;}while(l < n and (*this)[l] == 0) ++l;if(l > (n - 1) / k or l == n) return *this = F(n);T c = (*this)[l];(*this).erase((*this).begin(), (*this).begin() + l);(*this) /= c;(*this).log_inplace();(*this).resize(n - l * k);(*this) *= k;(*this).exp_inplace();(*this) *= c.pow(k);(*this).insert((*this).begin(), l * k, 0);return *this;}F pow(const long long k) const { return F(*this).pow_inplace(k); }// Ο(NlogN)F sqrt(int deg = -1) const {auto SQRT = [&](T t) {int mod = T::mod();if(t == 0 or t == 1) return t;int v = (mod - 1) / 2;if(t.pow(v) != 1) return T(-1);int q = mod - 1, m = 0;while(~q & 1) q >>= 1, m++;std::mt19937 mt;T z = mt();while(z.pow(v) != mod - 1) z = mt();T c = z.pow(q), u = t.pow(q), r = t.pow((q + 1) / 2);for(; m > 1; m--) {T tmp = u.pow(1 << (m - 2));if(tmp != 1) r = r * c, u = u * c * c;c = c * c;}return T(std::min(r.val(), mod - r.val()));};int n = (*this).size();if(deg == -1) deg = n;if((*this)[0] == 0) {for(int i = 1; i < n; i++) {if((*this)[i] != 0) {if(i & 1) return F(0);if(deg - i / 2 <= 0) break;auto ret = (*this);ret >>= i;ret.resize(n - i);ret = ret.sqrt(deg - i / 2);if(ret.empty()) return F(0);ret <<= (i / 2);ret.resize(deg);return ret;}}return F(deg);}auto sqr = SQRT((*this)[0]);if(sqr * sqr != (*this)[0]) return F(0);F ret{sqr};T ti = T(1) / T(2);for(int i = 1; i < deg; i <<= 1) {auto u = (*this);u.resize(i << 1);ret = (ret.inv(i << 1) * u + ret) * ti;}ret.resize(deg);return ret;}void sparse_pow(const int n, const int d, const T c, const int k, factorial<T> &fact) {F ret(n);T tmp = 1;if(k >= 0) {for(int i = 0; i < n; i += d) {ret[i] = fact.binom(k, i / d) * tmp;tmp *= c;}} else {for(int i = 0; i < n; i += d) {ret[i] = fact.binom(i / d - k - 1, -k - 1) * tmp;tmp *= -c;}}(*this) = ret;}void sparse_pow_inv(const int n, const int d, const T c, const int k, factorial<T> &fact) { return sparse_pow(n, d, c, -k, fact); }void stirling_first(int n, factorial<T> &fact) {if(!n) {*this = F{1};return;}int m = 1;F res(n + 1);res[1] = 1;for(int k = 30 - __builtin_clz(n); k >= 0; --k) {F as(m * 2 + 1), bs(m + 1);for(int i = 0; i <= m; i++)as[i] = fact.fac(i) * res[i];bs[m] = 1;for(int i = m - 1; i >= 0; i--)bs[i] -= bs[i + 1] * m;for(int i = 0; i <= m; i++)bs[m - i] *= fact.finv(i);F cs = as * bs, ds(m + 1);for(int i = 0; i <= m; i++)ds[i] = cs[m + i] * fact.finv(i);res *= ds;m <<= 1;if(n >> k & 1) {F g(n + 1);for(int i = 0; i <= m; i++) {g[i] -= res[i] * m;g[i + 1] += res[i];}res = g;m |= 1;}}*this = res;}void stirling_second(int n, factorial<T> &fact) {F f(n + 1), g(n + 1);for(int i = 0; i <= n; i++) {f[i] = T(i).pow(n) * fact.finv(i);g[i] = fact.finv(i) * (i % 2 ? -1 : 1);}f *= g;*this = f;}// return f(x + c)F taylor_shift(int c, factorial<T> &fact) const {F f(*this);int n = this->size();for(int i = 0; i < n; i++) f[i] *= fact.fac(i);reverse(f.begin(), f.end());F g(n, 1);T mul = 1;for(int i = 1; i < n; i++)g[i] = (mul *= c) * fact.finv(i);f *= g;reverse(f.begin(), f.end());for(int i = 0; i < n; i++) f[i] *= fact.finv(i);return f;}F taylor_shift(T c, factorial<T> &fact) const { return taylor_shift(c.val(), fact); }template <class U>std::vector<T> multipoint_evaluation(const std::vector<U> &p) {using fps = formal_power_series<T, mode>;int m = p.size();int n = 1 << std::max(atcoder::internal::ceil_pow2(m), 1);std::vector<fps> subproducts(2 * n, F{1}), rem(2 * n);for(int i = n; i < n + m; i++) subproducts[i] = fps({-p[i - n], 1});for(int i = n - 1; i; i--) {int x = subproducts[i << 1].size(), y = subproducts[i << 1 | 1].size();subproducts[i] = subproducts[i << 1];subproducts[i].resize(x + y - 1);subproducts[i] *= subproducts[i << 1 | 1];}rem[1] = *this;for(int i = 1; i < n; i++) {rem[i << 1] = rem[i] % subproducts[i << 1];rem[i << 1].shrink();rem[i << 1 | 1] = rem[i] % subproducts[i << 1 | 1];rem[i << 1 | 1].shrink();}std::vector<T> res(m);for(int i = 0; i < m; i++) res[i] = (!rem[i + n].empty() ? rem[i + n][0] : 0);return res;}};#line 3 "/home/nok0/documents/programming/library/math/modint_iostream.hpp"#line 5 "/home/nok0/documents/programming/library/math/modint_iostream.hpp"template<int m>std::istream &std::operator>>(std::istream &is, atcoder::static_modint<m> &a) {long long v;is >> v;a = v;return is;}template<int m>std::istream &std::operator>>(std::istream &is, atcoder::dynamic_modint<m> &a) {long long v;is >> v;a = v;return is;}template<int m>std::ostream &std::operator<<(std::ostream &os, const atcoder::static_modint<m> &a) { return os << a.val(); }template<int m>std::ostream &std::operator<<(std::ostream &os, const atcoder::dynamic_modint<m> &a) { return os << a.val(); }#line 2 "/home/nok0/documents/programming/library/template/header.hpp"#include <bits/stdc++.h>#line 3 "/home/nok0/documents/programming/library/template/def_const.hpp"const int inf = 1000000000;const long long INF = 1000000000000000000ll;#line 4 "/home/nok0/documents/programming/library/template/debug.hpp"namespace viewer {void view(const long long &e) {if(e == INF)std::cerr << "INF";else if(e == -INF)std::cerr << "-INF";elsestd::cerr << e;}void view(const int &e) {if(e == inf)std::cerr << "inf";else if(e == -inf)std::cerr << "-inf";elsestd::cerr << e;}template <typename T>void view(const T &e) {std::cerr << e;}template <typename T, typename U>void view(const std::pair<T, U> &p) {std::cerr << "(";view(p.first);std::cerr << ", ";view(p.second);std::cerr << ")";}template <class T0, class T1, class T2>void view(const std::tuple<T0, T1, T2> &p) {std::cerr << "(";view(std::get<0>(p));std::cerr << ", ";view(std::get<1>(p));std::cerr << ", ";view(std::get<2>(p));std::cerr << ")";}template <class T0, class T1, class T2, class T3>void view(const std::tuple<T0, T1, T2, T3> &p) {std::cerr << "(";view(std::get<0>(p));std::cerr << ", ";view(std::get<1>(p));std::cerr << ", ";view(std::get<2>(p));std::cerr << ", ";view(std::get<3>(p));std::cerr << ")";}template <typename T>void view(const std::set<T> &s) {if(s.empty()) {std::cerr << "{ }";return;}std::cerr << "{ ";for(auto &t : s) {view(t);std::cerr << ", ";}std::cerr << "\b\b }";}template <typename T>void view(const std::unordered_set<T> &s) {if(s.empty()) {std::cerr << "{ }";return;}std::cerr << "{ ";for(auto &t : s) {view(t);std::cerr << ", ";}std::cerr << "\b\b }";}template <typename T>void view(const std::multiset<T> &s) {if(s.empty()) {std::cerr << "{ }";return;}std::cerr << "{ ";for(auto &t : s) {view(t);std::cerr << ", ";}std::cerr << "\b\b }";}template <typename T>void view(const std::unordered_multiset<T> &s) {if(s.empty()) {std::cerr << "{ }";return;}std::cerr << "{ ";for(auto &t : s) {view(t);std::cerr << ", ";}std::cerr << "\b\b }";}template <typename T>void view(const std::vector<T> &v) {if(v.empty()) {std::cerr << "{ }";return;}std::cerr << "{ ";for(const auto &e : v) {view(e);std::cerr << ", ";}std::cerr << "\b\b }";}template <typename T, std::size_t ary_size>void view(const std::array<T, ary_size> &v) {if(v.empty()) {std::cerr << "{ }";return;}std::cerr << "{ ";for(const auto &e : v) {view(e);std::cerr << ", ";}std::cerr << "\b\b }";}template <typename T>void view(const std::vector<std::vector<T>> &vv) {std::cerr << "{\n";for(const auto &v : vv) {std::cerr << "\t";view(v);std::cerr << '\n';}std::cerr << "}";}template <typename T, typename U>void view(const std::vector<std::pair<T, U>> &v) {std::cerr << "{\n";for(const auto &c : v) {std::cerr << "\t(";view(c.first);std::cerr << ", ";view(c.second);std::cerr << ")\n";}std::cerr << "}";}template <class T0, class T1, class T2>void view(const std::vector<std::tuple<T0, T1, T2>> &v) {if(v.empty()) {std::cerr << "{ }";return;}std::cerr << '{';for(const auto &t : v) {std::cerr << "\n\t";view(t);std::cerr << ",";}std::cerr << "\n}";}template <class T0, class T1, class T2, class T3>void view(const std::vector<std::tuple<T0, T1, T2, T3>> &v) {if(v.empty()) {std::cerr << "{ }";return;}std::cerr << '{';for(const auto &t : v) {std::cerr << "\n\t";view(t);std::cerr << ",";}std::cerr << "\n}";}template <typename T, typename U>void view(const std::map<T, U> &m) {std::cerr << "{\n";for(const auto &t : m) {std::cerr << "\t[";view(t.first);std::cerr << "] : ";view(t.second);std::cerr << '\n';}std::cerr << "}";}template <typename T, typename U>void view(const std::unordered_map<T, U> &m) {std::cerr << "{\n";for(const auto &t : m) {std::cerr << "\t[";view(t.first);std::cerr << "] : ";view(t.second);std::cerr << '\n';}std::cerr << "}";}} // namespace viewer// when compiling : g++ foo.cpp -DLOCAL#ifdef LOCALvoid debug_out() {}template <typename Head, typename... Tail>void debug_out(Head H, Tail... T) {viewer::view(H);std::cerr << ", ";debug_out(T...);}#define debug(...) \do { \std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \debug_out(__VA_ARGS__); \std::cerr << "\b\b]\n"; \} while(0)#define dump(x) \do { \std::cerr << __LINE__ << " " << #x << " : "; \viewer::view(x); \std::cerr << '\n'; \} while(0)#else#define debug(...) (void(0))#define dump(x) (void(0))#endif#line 3 "/home/nok0/documents/programming/library/template/def_name.hpp"#define pb push_back#define eb emplace_back#define fi first#define se second#define SZ(x) ((int)(x).size())#define all(x) (x).begin(), (x).end()#define rall(x) (x).rbegin(), (x).rend()#define popcnt(x) __builtin_popcountll(x)template <class T = int>using V = std::vector<T>;template <class T = int>using VV = std::vector<std::vector<T>>;template <class T>using pqup = std::priority_queue<T, std::vector<T>, std::greater<T>>;using ll = long long;using ld = long double;using int128 = __int128_t;using pii = std::pair<int, int>;using pll = std::pair<long long, long long>;#line 3 "/home/nok0/documents/programming/library/template/fast_io.hpp"struct fast_io {fast_io() {std::ios::sync_with_stdio(false);std::cin.tie(nullptr);std::cout << std::fixed << std::setprecision(15);}} fast_io_;#line 3 "/home/nok0/documents/programming/library/template/input.hpp"template <class T, class U>std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {is >> p.first >> p.second;return is;}template <class T>std::istream &operator>>(std::istream &is, std::vector<T> &v) {for(T &i : v) is >> i;return is;}std::istream &operator>>(std::istream &is, __int128_t &a) {std::string s;is >> s;__int128_t ret = 0;for(int i = 0; i < (int)s.length(); i++)if('0' <= s[i] and s[i] <= '9')ret = 10 * ret + s[i] - '0';a = ret * (s[0] == '-' ? -1 : 1);return is;}namespace scanner {void scan(int &a) { std::cin >> a; }void scan(long long &a) { std::cin >> a; }void scan(std::string &a) { std::cin >> a; }void scan(char &a) { std::cin >> a; }void scan(char a[]) { std::ignore = std::scanf("%s", a); }void scan(double &a) { std::cin >> a; }void scan(long double &a) { std::cin >> a; }template <class T, class U>void scan(std::pair<T, U> &p) { std::cin >> p; }template <class T>void scan(std::vector<T> &a) { std::cin >> a; }void INPUT() {}template <class Head, class... Tail>void INPUT(Head &head, Tail &...tail) {scan(head);INPUT(tail...);}} // namespace scanner#define VEC(type, name, size) \std::vector<type> name(size); \scanner::INPUT(name)#define VVEC(type, name, h, w) \std::vector<std::vector<type>> name(h, std::vector<type>(w)); \scanner::INPUT(name)#define INT(...) \int __VA_ARGS__; \scanner::INPUT(__VA_ARGS__)#define LL(...) \long long __VA_ARGS__; \scanner::INPUT(__VA_ARGS__)#define STR(...) \std::string __VA_ARGS__; \scanner::INPUT(__VA_ARGS__)#define CHAR(...) \char __VA_ARGS__; \scanner::INPUT(__VA_ARGS__)#define DOUBLE(...) \double __VA_ARGS__; \scanner::INPUT(__VA_ARGS__)#define LD(...) \long double __VA_ARGS__; \scanner::INPUT(__VA_ARGS__)#line 3 "/home/nok0/documents/programming/library/template/math.hpp"template <class T, class U>inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; }template <class T, class U>inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; }template <class T>T divup(T x, T y) { return (x + y - 1) / y; }template <class T>T POW(T a, long long n) {T ret = 1;while(n) {if(n & 1) ret *= a;a *= a;n >>= 1;}return ret;}long long POW(long long a, long long n, const int mod) {long long ret = 1;a = (a % mod + mod) % mod;while(n) {if(n & 1) (ret *= a) %= mod;(a *= a) %= mod;n >>= 1;}return ret;}template <class T, class F>T bin_search(T ok, T ng, const F &f) {while(abs(ok - ng) > 1) {T mid = (ok + ng) >> 1;(f(mid) ? ok : ng) = mid;}return ok;}template <class T, class F>T bin_search(T ok, T ng, const F &f, int loop) {for(int i = 0; i < loop; i++) {T mid = (ok + ng) / 2;(f(mid) ? ok : ng) = mid;}return ok;}#line 3 "/home/nok0/documents/programming/library/template/output.hpp"template <class T, class U>std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {os << p.first << " " << p.second;return os;}template <class T>std::ostream &operator<<(std::ostream &os, const std::vector<T> &a) {for(int i = 0; i < int(a.size()); ++i) {if(i) os << " ";os << a[i];}return os;}std::ostream &operator<<(std::ostream &dest, __int128_t &value) {std::ostream::sentry s(dest);if(s) {__uint128_t tmp = value < 0 ? -value : value;char buffer[128];char *d = std::end(buffer);do {--d;*d = "0123456789"[tmp % 10];tmp /= 10;} while(tmp != 0);if(value < 0) {--d;*d = '-';}int len = std::end(buffer) - d;if(dest.rdbuf()->sputn(d, len) != len) {dest.setstate(std::ios_base::badbit);}}return dest;}template <class T>void print(const T a) { std::cout << a << '\n'; }template <class Head, class... Tail>void print(Head H, Tail... T) {std::cout << H << ' ';print(T...);}template <class T>void println(const T a) { std::cout << a << '\n'; }template <class T>void println(const std::vector<T> &a) {for(const auto &v : a)std::cout << v << '\n';}template <class Head, class... Tail>void println(Head H, Tail... T) {std::cout << H << '\n';println(T...);}void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); }void No() { std::cout << "No\n"; }void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); }void NO() { std::cout << "NO\n"; }#line 2 "/home/nok0/documents/programming/library/template/rep.hpp"#define foa(v, a) for (auto &v : a)#define repname(a, b, c, d, e, ...) e#define rep(...) repname(__VA_ARGS__, rep3, rep2, rep1, rep0)(__VA_ARGS__)#define rep0(x) for (int rep_counter = 0; rep_counter < (x); ++rep_counter)#define rep1(i, x) for (int i = 0; i < (x); ++i)#define rep2(i, l, r) for (int i = (l); i < (r); ++i)#define rep3(i, l, r, c) for (int i = (l); i < (r); i += (c))#define repsname(a, b, c, ...) c#define reps(...) repsname(__VA_ARGS__, reps1, reps0)(__VA_ARGS__)#define reps0(x) for (int reps_counter = 1; reps_counter <= (x); ++reps_counter)#define reps1(i, x) for (int i = 1; i <= (x); ++i)#define rrepname(a, b, c, ...) c#define rrep(...) rrepname(__VA_ARGS__, rrep1, rrep0)(__VA_ARGS__)#define rrep0(x) for (int rrep_counter = (x)-1; rrep_counter >= 0; --rrep_counter)#define rrep1(i, x) for (int i = (x)-1; i >= 0; --i)#line 3 "/home/nok0/documents/programming/library/template/string_converter.hpp"struct string_converter {char start = 0;char type(const char &c) const { return (islower(c) ? 'a' : isupper(c) ? 'A' :isdigit(c) ? '0' :0); }int convert(const char &c) {if(!start) start = type(c);return c - start;}int convert(const char &c, const std::string &chars) { return chars.find(c); }template <typename T>auto convert(const T &v) {std::vector<decltype(convert(v[0]))> ret;ret.reserve(size(v));for(auto &&e : v) ret.emplace_back(convert(e));return ret;}template <typename T>auto convert(const T &v, const std::string &chars) {std::vector<decltype(convert(v[0], chars))> ret;ret.reserve(size(v));for(auto &&e : v) ret.emplace_back(convert(e, chars));return ret;}int operator()(const char &v, char s = 0) {start = s;return convert(v);}int operator()(const char &v, const std::string &chars) { return convert(v, chars); }template <typename T>auto operator()(const T &v, char s = 0) {start = s;return convert(v);}template <typename T>auto operator()(const T &v, const std::string &chars) { return convert(v, chars); }} toint;#line 3 "/home/nok0/documents/programming/library/template/vector.hpp"template <class T>int lb(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); }template <class T>int ub(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); }template <class T>void UNIQUE(std::vector<T> &a) {std::sort(a.begin(), a.end());a.erase(std::unique(a.begin(), a.end()), a.end());}template <class T>std::vector<T> press(std::vector<T> &a) {auto res = a;UNIQUE(res);for(auto &v : a)v = lb(res, v);return res;}#define SORTname(a, b, c, ...) c#define SORT(...) SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__)#define SORT0(a) std::sort((a).begin(), (a).end())#define SORT1(a, c) std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; })template <class T>void ADD(std::vector<T> &a, const T x = 1) {for(auto &v : a) v += x;}template <class T>void SUB(std::vector<T> &a, const T x = 1) {for(auto &v : a) v -= x;}template <class T>struct cum_vector {public:cum_vector() = default;template <class U>cum_vector(const std::vector<U> &vec) : cum((int)vec.size() + 1) {for(int i = 0; i < (int)vec.size(); i++)cum[i + 1] = cum[i] + vec[i];}T prod(int l, int r) {return cum[r] - cum[l];}private:std::vector<T> cum;};std::vector<std::pair<char, int>> rle(const std::string &s) {const int n = s.size();std::vector<std::pair<char, int>> ret;ret.reserve(n);for(int l = 0; l < n;) {int r = l + 1;for(; r < n and s[l] == s[r]; r++) {}ret.emplace_back(s[l], r - l);l = r;}return ret;}template <class T>std::vector<std::pair<T, int>> rle(const std::vector<T> &v) {const int n = v.size();std::vector<std::pair<T, int>> ret;ret.reserve(n);for(int l = 0; l < n;) {int r = l + 1;for(; r < n and v[l] == v[r]; r++) {}ret.emplace_back(v[l], r - l);l = r;}return ret;}std::vector<int> iota(int n) {std::vector<int> p(n);std::iota(p.begin(), p.end(), 0);return p;}#line 12 "/home/nok0/documents/programming/library/template/all"using namespace std;#line 4 "a.cpp"using mint = atcoder::modint998244353;using fps = formal_power_series<mint, FAST>;void main_();int main() {int t = 1;while(t--) main_();}ll naive(ll n, ll m) {V<> p;ll ret = 0;auto dfs = [&](auto dfs) -> void {if(SZ(p) == n) {V<> c = p;rep(i, n) c[i] -= i;auto rv = rle(c);ll sc = 1;for(auto q : rv) sc *= q.second;ret += sc;return;}reps(i, m) {p.pb(i);dfs(dfs);p.pop_back();}};dfs(dfs);return ret;}void main_() {INT(n);LL(m);vector f(n + 1, mint(0));f[1] = 1;mint s1 = 1, s0 = 1;rep(i, 2, n + 1) {f[i] = i;f[i] += s1 - s0 * i;s1 += f[i] * i;s0 += f[i];}fps g(n + 1);reps(i, n) if(m - i + 1 > 0) g[i] = f[i] * (m - i + 1);fps h(n + 1);h[0] = 1;h -= g;print(h.inv().back());}