#include #include using namespace std; using namespace atcoder; typedef modint998244353 mint; typedef long long ll; #define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++) #define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--) template bool chmin(T &a, const T &b) { if (a <= b) return false; a = b; return true; } template bool chmax(T &a, const T &b) { if (a >= b) return false; a = b; return true; } //defmodfact const int COMinitMAX = 998244; mint fact[COMinitMAX+1], factinv[COMinitMAX+1]; void modfact(){ fact[0] = 1; for (int i=1; i<=COMinitMAX; i++){ fact[i] = fact[i-1] * i; } factinv[COMinitMAX] = fact[COMinitMAX].inv(); for (int i=COMinitMAX-1; i>=0; i--){ factinv[i] = factinv[i+1] * (i+1); } } mint cmb(int a, int b){ if (a poly_inv(vector &a, int M = -314159265){ if (M == -314159265) M = (int)a.size(); else if (M <= 0) return {}; int n = a.size(); mint r = a[0].pow((ll)(mint::mod())-2); int m = 1; vector res = {r}; while (m < M){ vector f = a; f.resize(2 * m); vector g = res; g.resize(2 * m); internal::butterfly(f); internal::butterfly(g); for (int i=0; i<2*m; i++){ f[i] = f[i] * g[i]; } internal::butterfly_inv(f); for (int i=0; i poly_log(vector &a, int M = -314159265){ if (M == -314159265) M = (int)a.size(); else if (M <= 0) return {}; int n = a.size(); if (n == 1) return vector(M, 0); vector b(n-1); for (int i=0; i t = convolution(b, poly_inv(a, M)); vector ret(M); for (int i=0; i poly_exp(vector &a, int M = -314159265){ if (M == -314159265) M = (int)a.size(); else if (M <= 0) return {}; int n = a.size(); int m = 1; vector res = {1}; while (m < M){ vector f(2*m); for (int i=0; i v = poly_log(res, 2*m); vector w(2*m); for (int i=0; i<2*m; i++) w[i] = f[i] - v[i]; w[0] += 1; vector g = convolution(res, w); res.insert(res.end(), g.begin()+m, g.begin()+2*m); m <<= 1; } res.resize(M); return res; } int main(){ modfact(); int n, k; cin >> n >> k; vector g(n+1); rep(i,1,n+1){ if (k%i == 0){ g[i] = mint(i).inv(); } } vector f = poly_exp(g); mint ans = f[n] * fact[n] * factinv[k]; cout << ans.val() << endl; }