#include using namespace std; //#pragma GCC optimize("Ofast") #define rep(i,n) for(ll i=0;i=0;i--) #define perl(i,r,l) for(ll i=r-1;i>=l;i--) #define all(x) (x).begin(),(x).end() #define CST(x) cout<> #define rev(x) reverse(x); using ll=long long; using vl=vector; using vvl=vector>; using pl=pair; using vpl=vector; using vvpl=vector; const ll MOD=1000000007; const ll MOD9=998244353; const int inf=1e9+10; const ll INF=4e18; const ll dy[9]={1,0,-1,0,1,1,-1,-1,0}; const ll dx[9]={0,1,0,-1,1,-1,1,-1,0}; template inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; } const int mod = MOD9; const int max_n = 2000050; 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; } bool operator==(const mint &p) const { return x == p.x; } bool operator!=(const mint &p) const { return x != p.x; } // 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, mint& a) { return is >> a.x;} ostream& operator<<(ostream& os, const mint& a) { return os << a.x;} using vm=vector; using vvm=vector; 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]; } }comb(max_n); unordered_map memo; mint PR(ll t){ if(memo.count(t))return memo[t]; else return memo[t]=mint(3).pow(t); } unordered_map memo2; mint INV(mint p){ if(memo2.count(p.x))return memo2[p.x]; else return memo2[p.x]=p.pow(MOD9-2); } namespace NTT { //MOD9のNTT auto c=NTT::mul(a,b)で受け取り。 vector tmp; size_t sz = 1; mint PrimitiveRoot=3; struct NTTPart { static std::vector ntt(std::vector a, bool inv = false) { size_t mask = sz - 1; size_t p = 0; for (size_t i = sz >> 1; i >= 1; i >>= 1) { auto& cur = (p & 1) ? tmp : a; auto& nex = (p & 1) ? a : tmp; mint e = PR((MOD9 - 1) / sz * i); if (inv) e = INV(e); mint w = 1; for (size_t j = 0; j < sz; j += i) { for (size_t k = 0; k < i; ++k) { nex[j + k] = cur[((j << 1) & mask) + k] + cur[(((j << 1) + i) & mask) + k] * w; } w *= e; } ++p; } if (p & 1) std::swap(a, tmp); if (inv) { mint invSz = INV(mint(sz)); for (size_t i = 0; i < sz; ++i) a[i] *= invSz; } return a; } static std::vector mul(std::vector a, std::vector b) { a = ntt(a); b = ntt(b); for (size_t i = 0; i < sz; ++i) a[i] = a[i] * b[i]; a = ntt(a, true); return a; } }; std::vector mul(std::vector a, std::vector b) { size_t m = a.size() + b.size() - 1; sz = 1; while (m > sz) sz <<= 1; tmp.resize(sz); a.resize(sz, 0); b.resize(sz, 0); vector c=NTTPart::mul(a, b); c.resize(m); return c; } }; int main(){ ll n,m;cin >> n >> m; vl b(n);rep(i,n)cin >> b[i]; ll f=min_element(all(b))-b.begin(); ll height=b[f];rep(i,n)b[i]-=height; vl left(n),right(n); for(ll j=f-1;j>=0;j--){ /*if(b[j]m)continue; dp[i+ret]=comb.ifact[i]*comb.ifact[ret]; } //rep(i,m+1)cout << dp[i] <<" ";cout << endl; for(ll j=1;jm)continue; ndp[k*2+left[j]+right[j]]=comb.ifact[k+left[j]]*comb.ifact[k+right[j]]; } dp=NTT::mul(dp,ndp); dp.resize(m+1); } cout << dp[m]*comb.fact[m] << endl; }