#include #include #include #include #define rep(i,a,b) for(int i=(a);i<(b);i++) #define rrep(i,a,b) for(int i=(b)-1;i>=(a);i--) #define all(x) begin(x),end(x) #define sz(x) (int)(x).size() using namespace std; using namespace atcoder; using ll=long long; using ld=long double; using vll=vector; using vvll=vector; using vi=vector; using vvi=vector; using pll=pair; using pi=pair; // using mint=modint998244353; // using mint=modint1000000007; // using mint2=static_modint<2>; // using BoostPoint=boost::polygon::point_data; // using Voronoi=boost::polygon::voronoi_diagram; #line 2 "modint/modint-2-61m1.hpp" #include #include using namespace std; struct modint_2_61m1 { using M = modint_2_61m1; using u64 = unsigned long long; using u128 = __uint128_t; static constexpr u64 mod = (1uLL << 61) - 1; u64 x; static constexpr u64 modulo(u128 y) { u64 val = (y >> 61) + (y & mod); return val >= mod ? val - mod : val; } modint_2_61m1() : x(0) {} modint_2_61m1(long long _x) { long long y = _x % (long long)mod; if (y < 0) y += mod; x = y; } static M raw(u64 y) { M res; res.x = y; return res; } u64 get() const { return x; } static u64 get_mod() { return mod; } friend M operator+(const M& l, const M& r) { u64 y = l.x + r.x; if (y >= mod) y -= mod; return raw(y); } friend M operator-(const M& l, const M& r) { u64 y = l.x - r.x; if (y >= mod) y += mod; return raw(y); } friend M operator*(const M& l, const M& r) { return raw(modulo(u128(l.x) * r.x)); } friend M operator/(const M& l, const M& r) { return l * r.inverse(); } M& operator+=(const M& r) { return *this = *this + r; } M& operator-=(const M& r) { return *this = *this - r; } M& operator*=(const M& r) { return *this = *this * r; } M& operator/=(const M& r) { return *this = *this / r; } M operator-() const { return raw(x ? mod - x : u64{0}); } M operator+() const { return *this; } M pow(u64 e) const { M res{1}, a{*this}; while (e) { if (e & 1) res = res * a; a = a * a; e >>= 1; } return res; } M inverse() const { assert(x != 0); return this->pow(mod - 2); } friend bool operator==(const M& l, const M& r) { return l.x == r.x; } friend bool operator!=(const M& l, const M& r) { return l.x != r.x; } friend ostream& operator<<(ostream& os, const M& r) { return os << r.x; } }; #line 2 "fps/sparse-fps.hpp" #include #include using namespace std; #line 2 "fps/formal-power-series.hpp" template struct FormalPowerSeries : vector { using vector::vector; using FPS = FormalPowerSeries; FPS &operator+=(const FPS &r) { if (r.size() > this->size()) this->resize(r.size()); for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i]; return *this; } FPS &operator+=(const mint &r) { if (this->empty()) this->resize(1); (*this)[0] += r; return *this; } FPS &operator-=(const FPS &r) { if (r.size() > this->size()) this->resize(r.size()); for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i]; return *this; } FPS &operator-=(const mint &r) { if (this->empty()) this->resize(1); (*this)[0] -= r; return *this; } FPS &operator*=(const mint &v) { for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v; return *this; } FPS &operator/=(const FPS &r) { if (this->size() < r.size()) { this->clear(); return *this; } int n = this->size() - r.size() + 1; if ((int)r.size() <= 64) { FPS f(*this), g(r); g.shrink(); mint coeff = g.back().inverse(); for (auto &x : g) x *= coeff; int deg = (int)f.size() - (int)g.size() + 1; int gs = g.size(); FPS quo(deg); for (int i = deg - 1; i >= 0; i--) { quo[i] = f[i + gs - 1]; for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j]; } *this = quo * coeff; this->resize(n, mint(0)); return *this; } return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev(); } FPS &operator%=(const FPS &r) { *this -= *this / r * r; shrink(); return *this; } FPS operator+(const FPS &r) const { return FPS(*this) += r; } FPS operator+(const mint &v) const { return FPS(*this) += v; } FPS operator-(const FPS &r) const { return FPS(*this) -= r; } FPS operator-(const mint &v) const { return FPS(*this) -= v; } FPS operator*(const FPS &r) const { return FPS(*this) *= r; } FPS operator*(const mint &v) const { return FPS(*this) *= v; } FPS operator/(const FPS &r) const { return FPS(*this) /= r; } FPS operator%(const FPS &r) const { return FPS(*this) %= r; } FPS operator-() const { FPS ret(this->size()); for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i]; return ret; } void shrink() { while (this->size() && this->back() == mint(0)) this->pop_back(); } FPS rev() const { FPS ret(*this); reverse(begin(ret), end(ret)); return ret; } FPS dot(FPS r) const { FPS ret(min(this->size(), r.size())); for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i]; return ret; } // 前 sz 項を取ってくる。sz に足りない項は 0 埋めする FPS pre(int sz) const { FPS ret(begin(*this), begin(*this) + min((int)this->size(), sz)); if ((int)ret.size() < sz) ret.resize(sz); return ret; } FPS operator>>(int sz) const { if ((int)this->size() <= sz) return {}; FPS ret(*this); ret.erase(ret.begin(), ret.begin() + sz); return ret; } FPS operator<<(int sz) const { FPS ret(*this); ret.insert(ret.begin(), sz, mint(0)); return ret; } FPS diff() const { const int n = (int)this->size(); FPS ret(max(0, n - 1)); mint one(1), coeff(1); for (int i = 1; i < n; i++) { ret[i - 1] = (*this)[i] * coeff; coeff += one; } return ret; } FPS integral() const { const int n = (int)this->size(); FPS ret(n + 1); ret[0] = mint(0); if (n > 0) ret[1] = mint(1); auto mod = mint::get_mod(); for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i); for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i]; return ret; } mint eval(mint x) const { mint r = 0, w = 1; for (auto &v : *this) r += w * v, w *= x; return r; } FPS log(int deg = -1) const { assert(!(*this).empty() && (*this)[0] == mint(1)); if (deg == -1) deg = (int)this->size(); return (this->diff() * this->inv(deg)).pre(deg - 1).integral(); } FPS pow(int64_t k, int deg = -1) const { const int n = (int)this->size(); if (deg == -1) deg = n; if (k == 0) { FPS ret(deg); if (deg) ret[0] = 1; return ret; } for (int i = 0; i < n; i++) { if ((*this)[i] != mint(0)) { mint rev = mint(1) / (*this)[i]; FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg); ret *= (*this)[i].pow(k); ret = (ret << (i * k)).pre(deg); if ((int)ret.size() < deg) ret.resize(deg, mint(0)); return ret; } if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0)); } return FPS(deg, mint(0)); } static void *ntt_ptr; static void set_fft(); FPS &operator*=(const FPS &r); void ntt(); void intt(); void ntt_doubling(); static int ntt_pr(); FPS inv(int deg = -1) const; FPS exp(int deg = -1) const; }; template void *FormalPowerSeries::ntt_ptr = nullptr; /** * @brief 多項式/形式的冪級数ライブラリ * @docs docs/fps/formal-power-series.md */ #line 8 "fps/sparse-fps.hpp" // g が sparse を仮定, f * g.inv() を計算 template FormalPowerSeries sparse_div(const FormalPowerSeries& f, const FormalPowerSeries& g, int deg = -1) { assert(g.empty() == false && g[0] != mint(0)); if (deg == -1) deg = f.size(); mint ig0 = g[0].inverse(); FormalPowerSeries s = f * ig0; s.resize(deg); vector> gs; for (int i = 1; i < (int)g.size(); i++) { if (g[i] != 0) gs.emplace_back(i, g[i] * ig0); } for (int i = 0; i < deg; i++) { for (auto& [j, g_j] : gs) { if (i + j >= deg) break; s[i + j] -= s[i] * g_j; } } return s; } template FormalPowerSeries sparse_inv(const FormalPowerSeries& f, int deg = -1) { assert(f.empty() == false && f[0] != mint(0)); if (deg == -1) deg = f.size(); vector> fs; for (int i = 1; i < (int)f.size(); i++) { if (f[i] != 0) fs.emplace_back(i, f[i]); } FormalPowerSeries g(deg); mint if0 = f[0].inverse(); if (0 < deg) g[0] = if0; for (int k = 1; k < deg; k++) { for (auto& [j, fj] : fs) { if (k < j) break; g[k] += g[k - j] * fj; } g[k] *= -if0; } return g; } template FormalPowerSeries sparse_log(const FormalPowerSeries& f, int deg = -1) { assert(f.empty() == false && f[0] == 1); if (deg == -1) deg = f.size(); vector> fs; for (int i = 1; i < (int)f.size(); i++) { if (f[i] != 0) fs.emplace_back(i, f[i]); } int mod = mint::get_mod(); static vector invs{1, 1}; while ((int)invs.size() <= deg) { int i = invs.size(); invs.push_back((-invs[mod % i]) * (mod / i)); } FormalPowerSeries g(deg); for (int k = 0; k < deg - 1; k++) { for (auto& [j, fj] : fs) { if (k < j) break; int i = k - j; g[k + 1] -= g[i + 1] * fj * (i + 1); } g[k + 1] *= invs[k + 1]; if (k + 1 < (int)f.size()) g[k + 1] += f[k + 1]; } return g; } template FormalPowerSeries sparse_exp(const FormalPowerSeries& f, int deg = -1) { assert(f.empty() or f[0] == 0); if (deg == -1) deg = f.size(); vector> fs; for (int i = 1; i < (int)f.size(); i++) { if (f[i] != 0) fs.emplace_back(i, f[i]); } int mod = mint::get_mod(); static vector invs{1, 1}; while ((int)invs.size() <= deg) { int i = invs.size(); invs.push_back((-invs[mod % i]) * (mod / i)); } FormalPowerSeries g(deg); if (deg) g[0] = 1; for (int k = 0; k < deg - 1; k++) { for (auto& [ip1, fip1] : fs) { int i = ip1 - 1; if (k < i) break; g[k + 1] += fip1 * g[k - i] * (i + 1); } g[k + 1] *= invs[k + 1]; } return g; } template FormalPowerSeries sparse_pow(const FormalPowerSeries& f, long long k, int deg = -1) { if (deg == -1) deg = f.size(); if (k == 0) { FormalPowerSeries g(deg); if (deg) g[0] = 1; return g; } int zero = 0; while (zero != (int)f.size() and f[zero] == 0) zero++; if (zero == (int)f.size() or __int128_t(zero) * k >= deg) { return FormalPowerSeries(deg, 0); } if (zero != 0) { FormalPowerSeries suf{begin(f) + zero, end(f)}; auto g = sparse_pow(suf, k, deg - zero * k); FormalPowerSeries h(zero * k, 0); copy(begin(g), end(g), back_inserter(h)); return h; } auto mod = mint::get_mod(); static vector invs{1, 1}; while ((int)invs.size() <= deg) { int i = invs.size(); invs.push_back((-invs[mod % i]) * (mod / i)); } vector> fs; for (int i = 1; i < (int)f.size(); i++) { if (f[i] != 0) fs.emplace_back(i, f[i]); } FormalPowerSeries g(deg); g[0] = f[0].pow(k); mint denom = f[0].inverse(); k %= mint::get_mod(); for (int a = 1; a < deg; a++) { for (auto& [i, f_i] : fs) { if (a < i) break; g[a] += f_i * g[a - i] * ((k + 1) * i - a); } g[a] *= denom * invs[a]; } return g; } /** * @brief sparse な形式的冪級数の演算 */ static const int M=55440; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int K,N; cin>>K>>N; int mx=N; while(mx==13||mx==17||mx==19||mx==23)mx--; int mn=M/mx; int D=M-K*mn; ll ans=(K==13||K==17||K==19||K==23); if(D>=0){ FormalPowerSeries P(D+1); rep(n,1,N+1){ if(n==13||n==17||n==19||n==23)continue; int i=M/n-mn; if(i<=D)P[i]=1; } FormalPowerSeries Q=sparse_pow(P,K,D+1); ans+=Q[D].get(); } cout<