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 = list(map(int, input().split(' ')))
    A = list(map(int, input().split(' ')))
    dp = [[0 for _ in range(K + 1)] for _ in range(N + 1)]
    for n in range(N + 1):
        dp[n][0] = 1
    for n in range(1, N + 1):
        dp_left = dp[n][0]  # dp[n][k - 1]
        for k in range(1, K + 1):
            val = dp_left + dp[n - 1][k]
            kk = k - A[n - 1] - 1
            if kk >= 0:
                val -= dp[n - 1][kk]
            val %= MOD
            dp[n][k] = val
            dp_left = val
    print(dp[N][K])


if __name__ == '__main__':
    main()