#pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include // cout, endl, cin #include // string, to_string, stoi #include // vector #include // min, max, swap, sort, reverse, lower_bound, upper_bound #include // pair, make_pair #include // tuple, make_tuple #include // int64_t, int*_t #include // printf #include // map #include // queue, priority_queue #include // set #include // stack #include // deque #include // unordered_map #include // unordered_set #include // bitset #include // isupper, islower, isdigit, toupper, tolower #include #include #include using namespace std; using namespace atcoder; #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define repi(i, a, b) for (int i = (int)(a); i < (int)(b); i++) typedef long long ll; typedef unsigned long long ull; const ll inf=1e18; using graph = vector > ; using P= pair; using vi=vector; using vvi=vector; using vll=vector; using vvll=vector; using vp=vector

; using vvp=vector; using vd=vector; using vvd =vector; //string T="ABCDEFGHIJKLMNOPQRSTUVWXYZ"; //string S="abcdefghijklmnopqrstuvwxyz"; //g++ main.cpp -std=c++17 -I . //cout < bool chmin(T& a, T b) { if (a > b) { a = b; return true; } else return false; } template bool chmax(T& a, T b) { if (a < b) { a = b; return true; } else return false; } // https://youtu.be/L8grWxBlIZ4?t=9858 // https://youtu.be/ERZuLAxZffQ?t=4807 : optimize // https://youtu.be/8uowVvQ_-Mo?t=1329 : division ll mod =998244353; struct mint { ll x; // typedef long long ll; mint(ll x=0):x((x%mod+mod)%mod){} mint operator-() const { return mint(-x);} mint& operator+=(const mint a) { if ((x += a.x) >= mod) x -= mod; return *this; } mint& operator-=(const mint a) { if ((x += mod-a.x) >= mod) x -= mod; return *this; } mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this;} mint operator+(const mint a) const { return mint(*this) += a;} mint operator-(const mint a) const { return mint(*this) -= a;} mint operator*(const mint a) const { return mint(*this) *= a;} mint pow(ll t) const { if (!t) return 1; mint a = pow(t>>1); a *= a; if (t&1) a *= *this; return a; } // for prime mod mint inv() const { return pow(mod-2);} mint& operator/=(const mint a) { return *this *= a.inv();} mint operator/(const mint a) const { return mint(*this) /= a;} }; istream& operator>>(istream& is, const mint& a) { return is >> a.x;} ostream& operator<<(ostream& os, const mint& a) { return os << a.x;} // combination mod prime // https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619 struct combination { vector fact, ifact; combination(int n):fact(n+1),ifact(n+1) { //assert(n < mod); fact[0] = 1; for (int i = 1; i <= n; ++i) fact[i] = fact[i-1]*i; ifact[n] = fact[n].inv(); for (int i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i; } mint operator()(int n, int k) { if (k < 0 || k > n) return 0; return fact[n]*ifact[k]*ifact[n-k]; } mint p(int n, int k) { return fact[n]*ifact[n-k]; } } c(500000); using vm=vector ; using vvm=vector ; ll sqrt_(ll x) { ll l = 0, r = ll(3e9)+1; while (l+1=0 && y>=0 && x struct Matrix { int h, w; vector> d; Matrix() {} Matrix(int h, int w, T val=0): h(h), w(w), d(h, vector(w,val)) {} Matrix& unit() { // assert(h == w); rep(i,h) d[i][i] = 1; return *this; } const vector& operator[](int i) const { return d[i];} vector& operator[](int i) { return d[i];} Matrix operator*(const Matrix& a) const { // assert(w == a.h); Matrix r(h, a.w); rep(i,h)rep(k,w)rep(j,a.w) { r[i][j] += d[i][k]*a[k][j]; } return r; } Matrix pow(long long t) const { // assert(h == w); if (!t) return Matrix(h,h).unit(); if (t == 1) return *this; Matrix r = pow(t>>1); r = r*r; if (t&1) r = r*(*this); return r; } // https://youtu.be/-j02o6__jgs?t=11273 /* mint only mint det() { assert(h == w); mint res = 1; rep(k,h) { for (int i = k; i < h; ++i) { if (d[i][k] == 0) continue; if (i != k) { swap(d[i],d[k]); res = -res; } } if (d[k][k] == 0) return 0; res *= d[k][k]; mint inv = mint(1)/d[k][k]; rep(j,h) d[k][j] *= inv; for (int i = k+1; i < h; ++i) { mint c = d[i][k]; for (int j = k; j < h; ++j) d[i][j] -= d[k][j]*c; } } return res; } //*/ }; using ve=vector; using vve=vector; void solve(int test){ int m,n; cin >> m >> n; vi a(n);rep(i,n)cin >> a[i]; sort(a.begin(),a.end()); vector

p; rep(i,n){ if(p.size()==0 || a[i]!=p.back().first)p.push_back(P(a[i],1)); else p.back().second++; } { vll v; for(auto u:p)v.push_back(u.second); vp p2; for(auto x:v){ if(p2.size()==0 || x!=p2.back().first)p2.push_back(P(x,1)); else p2.back().second++; } p=p2; } vm kai(n+1,1);for(int i=1; i<=n; i++)kai[i]=kai[i-1]*i; vll g(n+1,1); vll g2(n+1,1); for(int i=0; i<=n; i++){ mint now=1; for(auto u:p){ int num=u.first; mint now2=c(i,num)*kai[num]; now2=pow_pow(now2.x,u.second,mod); now*=now2; } now*=kai[i].inv(); g[i]=now.x; } for(int i=0; i<=n; i++){ mint now=1; now=pow_pow(mod-1,i,mod); now*=kai[i].inv(); g2[i]=now.x; } auto conv=convolution(g,g2); mint ans=0; for(int i=1; i<=n; i++){ ans+=kai[i]*conv[i]; } cout << ans << endl; } //g++ main.cpp -std=c++17 -I . int main(){cin.tie(0);ios::sync_with_stdio(false); int t=1; //cin >> t; rep(test,t)solve(test); }