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():

    N, K = map(int, input().split())
    a = list(map(int, input().split()))
    dp = [[0]*(K+1) for i in range(N+1)]
    import collections
    dp[0][K] = 1
    mod = 10**9 + 7
    # dp[i][j] i人目まで配って、残りがj個の方法の数
    s = [0]*(K+2)
    for i in range(1, N+1):
        tmp = 0
        for j in range(K, -1, -1):
            s[j] = (s[j+1] + dp[i-1][j]) % mod
        for j in range(K, -1, -1):
            tmp = s[j] - s[min(K, j+a[i-1]) + 1]
            tmp %= mod
            dp[i][j] = tmp

    print(dp[-1][0])


main()
