def perferct_solve(N,K,A):
    mod = 998244353

    diff = [A[i] for i in range(N)]
    cum = [A[i] for i in range(N)]
    S = A[0]
    for i in range(1,N):
        diff[i] = S - A[i]
        if diff[i] < 0:
            return 0
        S += A[i]
        cum[i] = S

    dp = [[0 for up in range(3*K+1)] for i in range(N)]

    for up in range(3*K+1):
        first = A[0] - up
        if -K<=first<=K:
            dp[0][up] = 1
        if up:
            dp[0][up] += dp[0][up-1]
            dp[0][up] %= mod

    for i in range(1,N):
        for up in range(3*K+1):
            if diff[i] and up<=A[i]+K:
                dp[i][up] += dp[i-1][0]
                dp[i][up] %= mod

            if up%2==diff[i] and diff[i]<=up<=cum[i]+2*K:
                dp[i][up] += dp[i-1][3*K] - dp[i-1][(up+diff[i])//2]
                dp[i][up] %= mod

            if diff[i]<=1 and diff[i]<=up<=cum[i]+2*K:
                pre_up_L = max(diff[i],-K+up-A[i])
                dp[i][up] += dp[i-1][(up+diff[i])//2] - dp[i-1][pre_up_L-1] * (pre_up_L>0)
                dp[i][up] %= mod

            if up:
                dp[i][up] += dp[i][up-1]
                dp[i][up] %= mod

    return dp[N-1][0]

N,K = map(int,input().split())
A = list(map(int,input().split()))
print(perferct_solve(N,K,A))