#include<bits/stdc++.h>
namespace {
#pragma GCC diagnostic ignored "-Wunused-function"
#include<atcoder/all>
#pragma GCC diagnostic warning "-Wunused-function"
using namespace std;
using namespace atcoder;
#define rep(i,n) for(int i = 0; i < (int)(n); i++)
#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--)
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
template<class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; }
template<class T> bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; }
using ll = long long;
using P = pair<int,int>;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;
using mint = modint998244353;

constexpr int FACT_SIZE = 1000000;
mint Fact[FACT_SIZE + 1];
mint iFact[FACT_SIZE + 1];
const auto fact_init = [] {
    Fact[0] = mint::raw(1);
    for(int i = 1; i <= FACT_SIZE; ++i) {
        Fact[i] = Fact[i-1] * i;
    }
    iFact[FACT_SIZE] = Fact[FACT_SIZE].inv();
    for(int i = FACT_SIZE; i; --i) {
        iFact[i-1] = iFact[i] * i;
    }
    return false;
}();

mint comb(int n, int k) {
    if (k == 0) return mint::raw(1);
    assert(n >= 0 && k >= 0);
    if (k > n) return mint::raw(0);
    return Fact[n] * iFact[n - k] * iFact[k];
}

mint icomb(int n, int k) {
    return iFact[n] * Fact[n - k] * Fact[k];
}

mint fact(int n) {return Fact[n];}
mint perm(int n, int k) {
    assert(0 <= n);
    return Fact[n] * iFact[n - k];
}

} int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m;
  cin >> n >> m;
  VI a(n);
  rep(i, n) cin >> a[i];
  VI b(n);
  int rest = m;
  rep(i, n - 1) {
    if (a[i] < a[i+1]) {
      int d = a[i+1] - a[i];
      b[i+1] += d;
      rest -= d;
    } else {
      int d = a[i] - a[i+1];
      b[0] += d;
      b[i+1] -= d;
      rest -= d;
    }
  }
  rep(i, n - 1) b[i+1] += b[i];
  if (b[0] > a[0]) {
    cout << 0 << '\n';
    return 0;
  }
  int T = a[0] - b[0];
  vector<mint> f(m + 1);
  f[0] = 1;
  rep(i, n - 1) {
    int d = abs(a[i+1] - a[i]);
    vector<mint> g(m + 1);
    rep(i, m + 1) g[i] = iFact[i] * iFact[d + i];
    f = convolution(f, g);
    f.resize(m + 1);
  }
  mint ans;
  rep(i, m + 1) {
    int r = rest - 2 * i;
    if (r < 0) break;
    int todo = T - i;
    int emp = r - todo;
    if (todo >= 0 && emp >= 0) {
      ans += f[i] * iFact[todo] * iFact[emp];
    }
  }
  ans *= Fact[m];
  cout << ans.val() << '\n';
}