#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[200010];
int main(){
    solve();
    int i,n,m; cin >> n >> m;
    for(i=0;i<n;i++) cin >> a[i];
    vector<mint> ff(m + 1),gg(m + 1),hh(m + 1);
    for(i=0;i<=m;i++){
        if(a[0] - a[1] + i>=0) ff[i] = fi[i]*fi[a[0] - a[1] + i];
        if(a[1] - a[2] + i>=0) gg[i] = fi[i]*fi[a[1] - a[2] + i];
        if(a[2] - a[3] + i>=0) hh[i] = fi[i]*fi[a[2] - a[3] + i];
    }
    ff = convolution(ff,gg);
    ff = convolution(ff,hh);
    mint ans = 0;
    for(i=0;i<=m;i++){
        if(a[3] - i>=0 && (m - a[0]) - i>=0) ans += ff[i]*fi[a[3] - i]*fi[m - a[0] - i];
    }
    ans *= f[m];
    cout << ans.val() << "\n";
}