def solve(N,K,A):
    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)

    dp = [{} for i in range(N-1)]
    stack = [(N-2,dp_S) for dp_S in range(10*K+10)]
    while stack:
        i,j = stack.pop()
        if j in dp[i]:
            continue
        dp[i][j] = [0 for k in range(6*K+2)]
        if not i:
            continue
        if diff[i]:
            stack.append((i-1,(j+diff[i+1]-2*K-1+diff[i])//2-diff[i]+2*K+1))
        if diff[i]<=1:
            for k in range(-2,1):
                stack.append((i-1,(j+diff[i+1]-2*K-1+k)//2+2*K+1))
            stack.append((i-1,(j+diff[i+1]-2*K-1-diff[i])//2+2*K+1))

    cum = [{sum:[0 for minus in range(6*K+2)] for sum in dp[i]} for i in range(N-1)]

    mod = 998244353

    for minus in range(6*K+2):
        for sum in dp[0]:
            dp_S = sum - minus
            real_S = diff[1] + dp_S - 2*K - 1
            first = diff[0] - minus
            if first==real_S and -K<=first<=K:
                dp[0][sum][minus] = 1

    for sum in dp[0]:
        cum[0][sum][0] = dp[0][sum][0]
        for minus in range(1,6*K+2):
            cum[0][sum][minus] = dp[0][sum][minus] + cum[0][sum][minus-1]
            cum[0][sum][minus] %= mod

    for i in range(1,N-1):
        for minus in range(6*K+2):
            for sum in dp[i]:
                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:
                        pre_dp_S = L - diff[i] + 2*K + 1
                        dp[i][sum][minus] += dp[i-1][pre_dp_S][0]
                        dp[i][sum][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(6*K+1,minus//2+3*K+diff[i])
                    if pre_minus_L<=pre_minus_R:
                        pre_sum = real_S//2+minus//2+2*K+1
                        dp[i][sum][minus] += cum[i-1][pre_sum][pre_minus_R] - cum[i-1][pre_sum][pre_minus_L] + dp[i-1][pre_sum][pre_minus_L]
                        dp[i][sum][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(6*K+1,M+diff[i])
                    if pre_minus_R>=pre_minus_L:
                        pre_sum = (real_S+minus-diff[i])//2+2*K+1
                        dp[i][sum][minus] += cum[i-1][pre_sum][pre_minus_R] - cum[i-1][pre_sum][pre_minus_L] + dp[i-1][pre_sum][pre_minus_L]
                        dp[i][sum][minus] %= mod

        for sum in cum[i]:
            cum[i][sum][0] = dp[i][sum][0]
            for minus in range(1,6*K+2):
                cum[i][sum][minus] = cum[i][sum][minus-1] + dp[i][sum][minus]
                cum[i][sum][minus] %= mod


    res = 0
    for real_S in range(-N*K,N*K+1):
        minus = 0
        i = N - 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:
                pre_dp_S = L - diff[i] + 2*K + 1
                res += dp[i-1][pre_dp_S][0]
                res %= 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(6*K+1,minus//2+3*K+diff[i])
            if pre_minus_L<=pre_minus_R:
                pre_sum = real_S//2+minus//2+2*K+1
                res += cum[i-1][pre_sum][pre_minus_R] - cum[i-1][pre_sum][pre_minus_L] + dp[i-1][pre_sum][pre_minus_L]
                res %= 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(6*K+1,M+diff[i])
            if pre_minus_R>=pre_minus_L:
                pre_sum = (real_S+minus-diff[i])//2+2*K+1
                res += cum[i-1][pre_sum][pre_minus_R] - cum[i-1][pre_sum][pre_minus_L] + dp[i-1][pre_sum][pre_minus_L]
                res %= mod

    return res

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

print(solve(N,K,A))