#include #include using namespace std; using namespace atcoder; typedef modint998244353 mint; typedef long long ll; //defmodfact const int COMinitMAX = 1234567; 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; } vector poly_pow_nonzero(vector &a, ll m, ll l){ int n = a.size(); mint bais = a[0].pow(m); mint invs; if (a[0].val() == 0) invs = 0; else invs = a[0].inv(); vector r(n); for (int i=0; i poly_pow(vector &a, ll m, ll l){ int n = a.size(); int ind = 0; for (int i=0; i= l){ return vector(l, 0); } vector ret(g*ind); vector b(n-ind); for (int i=0; i tmp; if (l-g*ind > 0) tmp = poly_pow_nonzero(b, m, l-g*ind); else tmp = {}; ret.insert(ret.end(), tmp.begin(), tmp.end()); return ret; } int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } vector multi_eval(vector x, vector a){ int n = x.size(); int siz = 1 << ceil_pow2(n); vector> g(2*siz, vector{1}); for (int i=0; i0; i--) g[i] = convolution(g[2*i], g[2*i+1]); vector f; for (int i=1; i<2*siz; i++){ if (i==1) f = a; else f = g[i>>1]; int fs = f.size(), gs = g[i].size(); int m = fs - gs + 1; vector v = {}, w = {}; if (m > 0){ vector ft(m); for (int j=0; j gt(gs); for (int j=0; j 1 && g[i][g[i].size() - 1] == 0){ g[i].pop_back(); } } vector ret(n); for (int i=0; i> n >> m; vector l(m); vector f(n+1); for (int i=0; i> l[i]; f[l[i]]++; } f[0]++; vector g = poly_pow(f, n+1, n+1); mint ans = g[n] * mint(n+1).inv(); cout << ans.val() << endl; }