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
mod = 10 ** 9 + 7

n, k = map(int, input().split())
a = tuple(int(x) for x in input().split())

d = tuple([0] * (k + k + 1) for _ in range(n + 1))
d[0][0] = 1

# もらう
for pind, lim in enumerate(a, 1):
    csum = [0]
    t = 0
    for cnt in range(k + 1):
        t += d[pind - 1][cnt]
        csum.append(t)
    for distributed in range(k + 1):
        d[pind][distributed] = (csum[distributed + 1] - csum[max(0, distributed - lim)]) % mod

print(d[n][k])