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 candies(k, a):
    mod = 10 ** 9 + 7
    cur = [0] * (k + 1)
    cur[0] = 1
    prefix = cur[:]
    nxt = cur[:]
    for x in a:
        for i in range(1, k + 1):
            prefix[i] = (prefix[i - 1] + cur[i]) % mod
        for i in range(1, k + 1):
            # nxt[i] = sum(cur[(i - x if i - x >= 0 else 0):i + 1]) % mod
            nxt[i] = (prefix[i] - (prefix[i - x - 1] if i - x - 1 >= 0 else 0)) % mod
        cur, nxt = nxt, cur
    return cur[k]


def main():
    n, k = [int(x) for x in input().split()]
    a = [int(x) for x in input().split()]
    return candies(k, a)


print(main())
