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 = list(map(int, input().split()))

cs_a, cnt = [0] * n, 0
for i in range(n):
    cnt += a[i]
    cs_a[i] = cnt
dp = [[0] * (k + 1) for i in range(n + 1)]

for i in range(n + 1):
    for j in range(k + 1):
        if j == 0:
            dp[i][j] = 1
        elif (i == 0) or (j > cs_a[i - 1]):
            dp[i][j] = 0
        elif j - a[i - 1] - 1 < 0:
            dp[i][j] = dp[i - 1][j] + dp[i][j - 1]
        else:
            dp[i][j] = dp[i - 1][j] + dp[i][j - 1] - dp[i - 1][j - a[i - 1] - 1]
        dp[i][j] %= 10 ** 9 + 7

print(dp[n][k])
