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
large_p = 10**9 + 7
from itertools import accumulate
from itertools import chain
def main():
    n, k = map(int, input().split())
    a = tuple(map(int, input().split()))
    dp = [[0] * (k+1) for _ in range(n+1)]
    dp[0][0] = 1
    for i1 in range(n):
        accum = tuple(chain([0], accumulate(dp[i1])))
        for i2 in range(k + 1):
            t = max(0, i2 - a[i1])
            dp[i1 + 1][i2] += accum[i2+1] - accum[t] + large_p
            dp[i1 + 1][i2] %= large_p

    print(dp[n][k])

if __name__ == '__main__':
    main()
