import sys
import itertools

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

MOD = 998_244_353

def is_balanced(A, Acum):
    for a, b in zip(A[1:], Acum[1:]):
        if a > b:
            return False
    return True

def main(N, K, A):
    S = [0] + list(itertools.accumulate(A))
    if not is_balanced(A, S):
        return 0
    MAX = K + 10
    # x 以下の数列は対策済
    dp = [0] * (MAX + MAX + 1)
    v = A[-1] - 1
    dp[v] = 1
    for n in range(N - 2, -1, -1):
        newdp = [0] * (MAX + MAX + 1)
        imos = [0] * (MAX + MAX + 1)
        for v in range(-MAX, MAX + 1):
            if not dp[v]:
                continue
            if v < S[n] + A[n] - 1:
                low = A[n]
            else:
                low = -K
            L, R = low, min(A[n], v // 2 + 1)
            if L <= R:
                newdp[v // 2] += dp[v] * (R - L + 1) % MOD
            L, R = max(low, v // 2 + 2), A[n]
            L, R = L - 1, R - 1
            if L <= R:
                imos[L] += dp[v]
                imos[R + 1] -= dp[v]
        for i in range(-MAX, MAX):
            imos[i] %= MOD
            imos[i + 1] += imos[i]
            newdp[i] += imos[i]
            newdp[i] %= MOD
        dp = newdp
    return sum(dp) % MOD

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

print(main(N, K, A))