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 f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = [0] * (k + 1)
    dp[0] = 1
    for a in a_s[:-1]:
        ndp = [0] * (k + 1)
        ndp[0] = s = dp[0] % md
        for j in range(1, a + 1):
            ndp[j] = s = (s + dp[j]) % md
        for j in range(a + 1, k + 1):
            ndp[j] = s = (s + dp[j] - dp[j - a - 1]) % md
        dp = ndp
    return sum(dp[k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(n, k, a_s))
