#include <bits/stdc++.h>
#include <atcoder/all>

using namespace std;
using namespace atcoder;

struct Fast {
  Fast() {
    std::cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << setprecision(10);
  }
} fast;

#define all(a) (a).begin(), (a).end()
#define contains(a, x) ((a).find(x) != (a).end())
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b)-1; i >= (a); i--)
#define writejoin(s, a) rep(_i, 0, (a).size()) cout << (a)[_i] << (_i + 1 < (int)(a).size() ? s : "\n");
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";

template <typename mint>
class Factorial {
 public:
  Factorial(int max) : n(max) {
    f = vector<mint>(n + 1);
    finv = vector<mint>(n + 1);
    f[0] = 1;
    for (int i = 1; i <= n; i++) f[i] = f[i - 1] * i;
    finv[n] = f[n].inv();
    for (int i = n; i > 0; i--) finv[i - 1] = finv[i] * i;
  }
  mint fact(int k) {
    assert(0 <= k && k <= n);
    return f[k];
  }
  mint fact_inv(int k) {
    assert(0 <= k && k <= n);
    return finv[k];
  }
  mint binom(int k, int r) {
    assert(0 <= k && k <= n);
    if (r < 0 || r > k) return 0;
    return f[k] * finv[r] * finv[k - r];
  }
  mint inv(int k) {
    assert(0 < k && k <= n);
    return finv[k] * f[k - 1];
  }

 private:
  int n;
  vector<mint> f, finv;
};

using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using mint = modint998244353;

int main() {
  int n, m;
  cin >> n >> m;
  vi b(n);
  rep(i, 0, n) cin >> b[i];

  rrep(i, 1, n) b[i] -= b[i - 1];
  int sum = 0;
  rep(i, 0, n) sum += b[i];
  if (sum > m) {
    cout << 0 << "\n";
  } else {
    b[0] -= m - sum;

    int sumabs = 0;
    rep(i, 0, n) sumabs += abs(b[i]);
    if (sumabs > m) {
      cout << 0 << "\n";
    } else {
      Factorial<mint> fact(100000);
      vector<mint> f{fact.fact(m)};
      rep(i, 0, n) {
        int v = abs(b[i]);
        vector<mint> g(m + 1, 0);
        for (int j = 0; v + 2 * j <= m; j++)
          g[v + 2 * j] = fact.fact_inv(j) * fact.fact_inv(v + j);
        f = convolution(f, g);
        f.resize(m + 1);
      }
      cout << f[m].val() << "\n";
    }
  }
}