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
N, K = map(int, input().split())
a = tuple(map(int, input().split()))

def main():
    l = [1 if a[0] >= j else 0 for j in range(K+1)]
    lt= [0] * (K+1)
    s = a[0]
    for i in range(1,N):
        lt, l = l, lt
        s += a[i]
        l[0] = 1
        t = 1
        for j in range(1, a[i]+1):
                t += lt[j]
                l[j] = t
        for j in range(a[i]+1, min(K+1, s+1)):
                t += (lt[j] - lt[j - a[i] - 1])
                l[j] = t
    return l[-1] % (10 ** 9 + 7)
            
print(main())
