#include<bits/stdc++.h>
using namespace std;
#include<atcoder/all>
using namespace atcoder;
using mint = modint998244353;
mint fac[200000], facinv[200000];
void init(){
  fac[0] = 1;
  for(int i = 1; i < 200000; i++) fac[i] = fac[i - 1] * i;
  facinv[200000 - 1] = 1 / fac[200000 - 1];
  for(int i = 200000 - 2; i >= 0; i--) facinv[i] = facinv[i + 1] * (i + 1);
}
int main(){
  init();
  int n, m;
  cin >> n >> m;
  vector<int> b(n);
  for(int i = 0; i < n; i++) cin >> b[i];
  if(n == 1){
    cout << (fac[m] * facinv[m - b[0]] * facinv[b[0]]).val() << endl;
    return 0;
  }
  vector<int> a(n - 1);
  for(int i = 0; i < n - 1; i++) a[i] = b[i + 1] - b[i];
  vector<mint> ret(1, 1);
  for(int i = 0; i < n - 1; i++){
    vector<mint> v(m + 1);
    for(int j = 0; j <= m; j++){
      if(a[i] + j < 0 || a[i] + 2 * j > m) continue;
      v[a[i] + 2 * j] = facinv[j] * facinv[a[i] + j];
    }
    ret = convolution(ret, v);
    ret.resize(m + 1);
  }
  int x = b[0] + b[n - 1];
  mint ans = 0;
  for(int i = 0; i * 2 <= x; i++){
    mint c = ret[x - 2 * i] * facinv[i] * facinv[m - x + i];
    ans += c;
  }
  ans *= fac[m];
  cout << ans.val() << endl;
}