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 minus in range(3*K+1)] for i in range(N)]

    for minus in range(3*K+1):
        first = A[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):
        for minus in range(3*K+1):

            if diff[i] and -K<=A[i]-minus<=K:
                dp[i][minus] += dp[i-1][0]
                dp[i][minus] %= mod

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

            if diff[i]<=1:
                pre_minus_L = max(diff[i],-K+minus-A[i])
                pre_minus_R = min((minus+diff[i])//2,K+minus-A[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 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()))

assert 2<=N<=1500
assert 1<=K<=1500
assert len(A)==N
for i in range(N):
    assert abs(A[i])<=K

print(perferct_solve(N,K,A))