There are N children, numbered 1, 2, \ldots, N.

They have decided to share K candies among themselves. Here, for each i (1 \leq i \leq N), Child i must receive between 0 and a_i candies (inclusive). Also, no candies should be left over.

Find the number of ways for them to share candies, modulo 10^9 + 7. Here, two ways are said to be different when there exists a child who receives a different number of candies.

Constraints

* All values in input are integers.
* 1 \leq N \leq 100
* 0 \leq K \leq 10^5
* 0 \leq a_i \leq K

Input

Input is given from Standard Input in the following format:


N K
a_1 a_2 \ldots a_N


Output

Print the number of ways for the children to share candies, modulo 10^9 + 7.

Examples

Input

3 4
1 2 3


Output

5


Input

1 10
9


Output

0


Input

2 0
0 0


Output

1


Input

4 100000
100000 100000 100000 100000


Output

665683269
def main():
    MOD = 10**9 + 7
    N, K = (int(i) for i in input().split())
    A = [int(i) for i in input().split()]
    dp = [[0]*(K+1) for i in range(N+1)]
    dp[0][0] = 1
    S = [0] * (K+2)
    for i in range(1, N+1):
        S[0] = 0
        for j in range(1, K+2):
            S[j] = (S[j-1] + dp[i-1][j-1]) % MOD
        # print(S)
        for j in range(K+1):
            """
            for k in range(A[i-1]+1):
                # i番目の子供がk個受け取る
                if j - k >= 0:
                    dp[i][j] = (dp[i][j] + dp[i-1][j-k]) % MOD
            """
            dp[i][j] = (S[j+1] - S[max(0, j-A[i-1])] + MOD) % MOD
    print(dp[N][K])
    # for i in range(N+1):
    #     print(*dp[i])


if __name__ == '__main__':
    main()
