#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <iostream>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <queue>
#include <algorithm>
#include <cmath>
#include <iomanip>
#include <random>
#include <stdio.h>
#include <fstream>
#include <cstdint>
using namespace std;

typedef long long ll;
const ll mod=998244353;

int main(){
    int N;
    long int K;
    cin>>N>>K;
    vector<int> A(N);
    for (int i=0;i<N;i++){
        cin>>A[i];
    }
    vector<long int> diff(N);
    vector<long int> cum(N);
    long int S = A[0];
    for (int i=1;i<N;i++){
        diff[i] = S - A[i];
        if (diff[i]<0){
            cout<<0<<endl;
            return 0;
        }
        S += A[i];
        cum[i] = S;
    }

    vector<vector<ll>> dp(N,vector<ll>(3*K+1,0));

    for (long int minus=0;minus<3*K+1;minus++){
        if (-K<=A[0]-minus && A[0]-minus<=K){
            dp[0][minus] = 1;
        }
    }
    //cout<<endl;

    long int pre_minus_L,pre_minus_R;

    for (int i=1;i<N;i++){
        for (long int minus=0;minus<3*K+1;minus++){

            if (diff[i]!=0 && minus<=A[i]+K){
                dp[i][minus] += dp[i-1][0];
                if (dp[i][minus]>=mod){
                    dp[i][minus] -= mod;
                }
            }

            if (minus%2==diff[i] and -K<=(cum[i]-minus)/2 and (cum[i]-minus)/2<=K){
                for (long int pre_minus=(minus/2)+diff[i]+1;pre_minus<3*K+1;pre_minus++){
                    dp[i][minus] += dp[i-1][pre_minus];
                    if (dp[i][minus]>=mod){
                    dp[i][minus] -= mod;
                    }
                }
            }

            if (diff[i]<=1 && diff[i]<=minus && minus<=cum[i]+2*K){
                pre_minus_L = max(diff[i],-K+minus-A[i]);
                pre_minus_R = min((minus+diff[i])/2,K+minus-A[i]);
                for (long int pre_minus=pre_minus_L;pre_minus<=pre_minus_R;pre_minus++){
                    dp[i][minus] += dp[i-1][pre_minus];
                    if (dp[i][minus]>=mod){
                    dp[i][minus] -= mod;
                    }
                }
            }

            //cout<<dp[i][minus]<<" ";
        }
        //cout<<endl;
    }
    cout<<dp[N-1][0]<<endl;
}