// clang-format off #include using namespace std; using ll = long long; using ld = long double; template using V = vector; using VI = V; using VL = V; using VS = V; template using PQ = priority_queue, greater>; using G = V; template using WG = V>>; #define overload4(_1,_2,_3,_4,name,...) name #define overload3(_1,_2,_3,name,...) name #define rep1(n) for(ll _=0;_<(n);++_) #define rep2(i,n) for(ll i=0;i<(n);++i) #define rep3(i,a,b) for(ll i=(a);i<(b);++i) #define rep4(i,a,b,c) for(ll i=(a);i<(b);i+=(c)) #define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__) #define rrep1(n) for(ll i=n-1;i>=0;--i) #define rrep2(i,n) for(ll i=n-1;i>=0;--i) #define rrep3(i,a,b) for(ll i=b-1;i>=a;--i) #define rrep(...) overload3(__VA_ARGS__,rrep3,rrep2,rrep1)(__VA_ARGS__) #define all(a) a.begin(),a.end() #define rall(a) a.rbegin(),a.rend() #define inside(h,w,y,x) (unsigned(y) inline bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; }return false; } template inline bool chmin(T& a, const T& b) { if (a > b) { a = b; return true; }return false; } inline void init() { cin.tie(nullptr); cout.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } template inline istream& operator>>(istream& is, V& v) { for (auto& a : v)is >> a; return is; } template inline istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template inline V vec(size_t a) { return V(a); } template inline V defvec(T def, size_t a) { return V(a, def); } template inline auto vec(size_t a, Ts... ts) { return V(ts...))>(a, vec(ts...)); } template inline auto defvec(T def, size_t a, Ts... ts) { return V(def, ts...))>(a, defvec(def, ts...)); } template inline void print(const T& a) { cout << a << "\n"; } template inline void print(const T& a, const Ts&... ts) { cout << a << " "; print(ts...); } template inline void print(const V& v) { for (int i = 0; i < v.size(); ++i)cout << v[i] << (i == v.size() - 1 ? "\n" : " "); } template inline void print(const V>& v) { for (auto& a : v)print(a); } template inline constexpr const T cum(const V& a, int l, int r) { return 0 <= l && l <= r && r < a.size() ? a[r] - (l == 0 ? 0 : a[l - 1]) : 0; }//[l,r] template inline constexpr const auto min(const T& v) { return *min_element(all(v)); } template inline constexpr const auto max(const T& v) { return *max_element(all(v)); } template inline V& operator++(V& v) { for (T& a : v)++a; return v; } template inline V& operator--(V& v) { for (T& a : v)--a; return v; } // clang-format on #include using namespace atcoder; using mint = atcoder::modint998244353; class combination { public: int n; ll c_mod; VL fac, finv, inv; combination(int n, ll c_mod) : n(n), c_mod(c_mod), fac(n), finv(n), inv(n) { fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (int i = 2; i < n; ++i) { fac[i] = fac[i - 1] * i % c_mod; inv[i] = c_mod - inv[c_mod % i] * (c_mod / i) % c_mod; finv[i] = finv[i - 1] * inv[i] % c_mod; } } ll operator()(int n, int k) { if (n < k) return 0; if (n < 0 || k < 0) return 0; return fac[n] * (finv[k] * finv[n - k] % c_mod) % c_mod; } }; int main() { init(); int m, n; cin >> m >> n; VI c(m); rep(i, n) { int a; cin >> a; --a; ++c[a]; } VI cc(n + 1); for (int x : c) ++cc[x]; V g(n + 1, 1); combination com(n + 10, MOD); rep(j, n + 1) if (cc[j] > 0) { int x = j, s = cc[j]; rep(i, 1, n + 1) { if (i - x >= 0) g[i] *= mint(com.fac[i] * com.finv[i - x]).pow(s); else g[i] = 0; } } mint ans = 0; rep(l, 1, n + 1) { mint tmp = 0; rep(i, 1, l + 1) { mint res = (mint)com.finv[i] * com.finv[l - i] * g[i]; tmp += res * ((l - i) & 1 ? -1 : 1); } ans += tmp * com.fac[l]; } print(ans.val()); return 0; }