#include <bits/stdc++.h>
#include <atcoder/convolution>
using namespace std;
const long long MOD = 998244353;
int main(){
  int N, M;
  cin >> N >> M;
  vector<int> B(N);
  for (int i = 0; i < N; i++){
    cin >> B[i];
  }
  vector<int> imos(N + 1, 0);
  int D = 0;
  for (int i = 0; i < N - 1; i++){
    if (B[i] < B[i + 1]){
      D += B[i + 1] - B[i];
      imos[i + 1] += B[i + 1] - B[i];
      imos[N] -= B[i + 1] - B[i];
    } else {
      D += B[i] - B[i + 1];
      imos[0] += B[i] - B[i + 1];
      imos[i + 1] -= B[i] - B[i - 1];
    }
  }
  for (int i = 0; i < N; i++){
    imos[i + 1] += imos[i];
  }
  if (D > M || imos[0] > B[0]){
    cout << 0 << endl;
  } else {
    int a = M - D;
    int b = B[0] - imos[0];
    if (b > a){
      cout << 0 << endl;
    } else {
      vector<long long> inv(M + 1);
      inv[1] = 1;
      for (int i = 2; i <= M; i++){
        inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
      }
      vector<long long> fact(M + 1);
      vector<long long> finv(M + 1);
      fact[0] = 1;
      finv[0] = 1;
      for (int i = 1; i <= M; i++){
        fact[i] = fact[i - 1] * i % MOD;
        finv[i] = finv[i - 1] * inv[i] % MOD;
      }
      vector<vector<long long>> f(3, vector<long long>(M + 1, 0));
      for (int i = 0; i < 3; i++){
        int d = abs(B[i] - B[i + 1]);
        for (int j = 0; j <= M - d; j++){
          f[i][j] = finv[j] * finv[d + j] % MOD;
        }
      }
      vector<long long> P(M + 1, 0);
      P[0] = 1;
      for (int i = 0; i < 3; i++){
        P = atcoder::convolution(P, f[i]);
        P.resize(M + 1);
      }
      long long ans = 0;
      for (int i = 0; i <= M; i++){
        if (a >= i * 2 && b >= i && a - i * 2 >= b - i){
          ans += P[i] * finv[b - i] % MOD * finv[a - b - i] % MOD * fact[M] % MOD;
        }
      }
      ans %= MOD;
      cout << ans << endl;
    }
  }
}