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

    diff = [A[0] 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]
    diff.append(0)

    sum_table = [0 for i in range(N)]
    sum_table[0] = diff[0] - diff[1] + 2*K + 1
    for i in range(1,N):
        sum_table[i] = 2 * sum_table[i-1] + diff[i] - diff[i+1] - (2*K+1)

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

    for minus in range(3*K+1):
        dp_S = sum_table[0] - minus
        real_S = diff[1] + dp_S - 2*K - 1
        first = diff[0] - minus
        if -K<=first<=K:
            dp[0][minus] = 1
        if minus:
            dp[0][minus] += dp[0][minus-1]
            dp[0][minus] %= mod

    for i in range(1,N):
        sum = sum_table[i]
        for minus in range(3*K+1):
            dp_S = sum - minus
            real_S = dp_S + diff[i+1] - 2*K - 1

            if diff[i]:
                L = max((real_S+minus+diff[i]+1)//2,-K+minus+diff[i])
                R = min((real_S+minus+diff[i])//2,K+minus+diff[i])
                if L==R:
                    dp[i][minus] += dp[i-1][0]
                    dp[i][minus] %= mod

            if minus%2==diff[i] and real_S%2==0 and -K<=real_S//2<=K:
                pre_minus_L = max(0,minus//2+1+diff[i])
                pre_minus_R = min(3*K,minus//2+3*K+diff[i])
                if pre_minus_L<=pre_minus_R:
                    dp[i][minus] += dp[i-1][pre_minus_R] - dp[i-1][pre_minus_L-1] * (pre_minus_L>0)
                    dp[i][minus] %= mod

            if diff[i]<=1 and (real_S+minus-diff[i])%2==0:
                m = max(0,-K+minus-diff[i]-(real_S+minus-diff[i])//2)
                M = min((minus-diff[i])//2,K+minus-diff[i]-(real_S+minus-diff[i])//2)
                pre_minus_L = max(0,m+diff[i])
                pre_minus_R = min(3*K,M+diff[i])
                if pre_minus_R>=pre_minus_L:
                    dp[i][minus] += dp[i-1][pre_minus_R] - dp[i-1][pre_minus_L-1] * (pre_minus_L>0)
                    dp[i][minus] %= mod

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

    return dp[N-1][0]

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