#include <iostream>
#include <vector>
#include <atcoder/modint>
#include <atcoder/convolution>

using namespace std;
using namespace atcoder;
using ll = long long;
using mint = modint998244353;
const int MX = 1000010;
mint f[MX],inv[MX],fi[MX];
constexpr ll mod = 998244353;
void solve(){
    inv[1] = 1;
    for(int i=2;i<MX;i++){
        inv[i] = mod - (mod/i)*inv[mod%i];
    }
    f[0] = fi[0] = 1;
    for(int i=1;i<MX;i++){
        f[i] = f[i-1]*i;
        fi[i] = fi[i-1]*inv[i];
    }
}

int a[2010],b[2010];
int main(){
    solve();
    int i,j,n,m; cin >> n >> m;
    for(i=0;i<n;i++) cin >> a[i];
    for(i=1;i<n;i++) b[i] = a[i] - a[i - 1]; 
    vector<mint> ff = {1};
    for(i=1;i<n;i++){
        vector<mint> g(m + 1);
        for(j=0;j<=m;j++){
            if(j + b[i]>=0) g[j] = fi[j]*fi[j + b[i]];
        }
        ff = convolution(ff,g);
        ff.resize(m + 1);
    }
    mint ans = 0;
    for(i=0;i<=m;i++){
        if(ff.size()>i && a[0]>=i && m - a[n - 1]>=i) ans += ff[i]*fi[a[0] - i]*fi[m - a[n - 1] - i];
    }
    ans *= f[m];
    cout << ans.val() << "\n";
}