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 = map(int,input().split())
    candies = list(map(int,input().split()))
    dp = [[0 for i in range(k+1)] for j in range(n+1)]
    dp[0][0] = 1
    for pos in range(1,n+1):
        for used in range(k+1):
            a = candies[pos-1]
            start = used
            end = min(start+a+1,k+1)
            dp[pos][start] += dp[pos-1][start]
            if end <= k:
                dp[pos][end] -= dp[pos-1][start]

        for used in range(1,k+1):
            dp[pos][used] += dp[pos][used-1]
            dp[pos][used] %= mod


    print(dp[-1][-1])


main()
