#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; const int m0 = m; VI a(n); rep(i, n) cin >> a[i]; int imn = min_element(all(a)) - a.begin(); if (![&]() ->bool { rrep(i, imn) if (a[i] < a[i+1]) return false; for(int i = imn + 1; i < n; i++) { if (a[i-1] > a[i]) return false; } return true; }()) { cout << 0 << '\n'; return 0; } vector<mint> f{1}; rep(i, n - 1) { int d = abs(a[i+1] - a[i]); m -= d; 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 rest = m - 2 * i; if (rest < 0) break; int todo = a[imn] - i; int emp = rest - todo; if (todo >= 0 && emp >= 0) { ans += f[i] * iFact[todo] * iFact[emp]; } } ans *= Fact[m0]; cout << ans.val() << '\n'; }