#include <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <deque>
#include <set>
#include <map>
#include <tuple>
#include <cmath>
#include <numeric>
#include <functional>
#include <cassert>
#include <atcoder/convolution>
#include <atcoder/modint>

#define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl;
#define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

using namespace std;
typedef long long ll;

template<typename T>
vector<vector<T>> vec2d(int n, int m, T v){
    return vector<vector<T>>(n, vector<T>(m, v));
}

template<typename T>
vector<vector<vector<T>>> vec3d(int n, int m, int k, T v){
    return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, v)));
}

template<typename T>
void print_vector(vector<T> v, char delimiter=' '){
    if(v.empty()) {
        cout << endl;
        return;
    }
    for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter;
    cout << v.back() << endl;
}

using mint = atcoder::modint998244353;

ostream& operator<<(ostream& os, const mint& m){
    os << m.val();
    return os;
}

#define N_MAX 200002
mint inv[N_MAX],fac[N_MAX],finv[N_MAX];

void init(){
    const ll MOD = mint::mod();
    fac[0]=1;fac[1]=1;
    finv[0]=1;finv[1]=1;
    inv[1]=1;
    for(int i=2;i<N_MAX;i++){
        inv[i]=mint(MOD)-inv[MOD%i]*(MOD/i);
        fac[i]=fac[i-1]*(ll) i;
        finv[i]=finv[i-1]*inv[i];
    }
}

mint comb(ll n, ll r){
    if(n < r){
        return mint(0);
    }else{
        return fac[n]*finv[r]*finv[n-r];
    }
}

vector<mint> all_prod(vector<vector<mint>> v){
    queue<vector<mint>> que;
    for(auto u: v) que.push(u);
    while(que.size() > 1){
        auto u0 = que.front(); que.pop();
        auto u1 = que.front(); que.pop();
        que.push(atcoder::convolution(u0, u1));
    }
    return que.front();
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(10) << fixed;
    init();
    int n, m; cin >> n >> m;
    vector<int> b(n);
    for(int i = 0; i < n; i++) cin >> b[i];
    vector<int> d(n+1);
    d[0] = b[0];
    for(int i = 0; i < n; i++){
        d[i] = b[i]-b[i-1];
    }
    d[n] = -b[n-1];
    ll pos_sum = 0, neg_sum = 0;
    for(int i = 1; i < n; i++){
        if(d[i] > 0){
            pos_sum += d[i];
        }
        if(d[i] < 0){
            neg_sum -= d[i];
        }
    }
    if(pos_sum + neg_sum > m){
        cout << 0 << endl;
        return 0;
    }
    

    vector<vector<mint>> u(n-1);
    for(int i = 1; i < n; i++){
        u[i-1].resize(m+1);
        for(int a = 0; abs(d[i])+2*a <= m; a++){
            u[i-1][abs(d[i])+2*a] = finv[abs(d[i])+a]*finv[a];
        }
    }

    auto w = all_prod(u);
    mint ans = 0;
    for(int a = 0; a*2+pos_sum+neg_sum <= m; a++){
        int x = a*2+pos_sum+neg_sum;
        int pos = b.back();
        int neg = b[0];
        if(pos_sum+a > pos || neg_sum+a > neg) continue;
        int rem = pos-(pos_sum+a);
        if(x+rem > m) continue;
        ans += comb(m, x+rem)*comb(x+rem, rem)*fac[x]*w[x];
    }
    cout << ans << endl;
}