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()))

MOD = 10 ** 9 + 7

dp = [[0 for _ in range(k+1)] for _ in range(n)]

dp[0][0] = 1
for j in range(1, a[0] + 1):
    dp[0][j] = 1

for i in range(1, n):
    dp[i][0] = 1
    for j in range(1, k+1):
        temp = dp[i-1][j]
        if j > 0:
            temp += dp[i][j-1]
        if j-a[i] > 0:
            temp -= dp[i-1][j-a[i]-1]
        dp[i][j] = (temp + MOD) % MOD

print(dp[n-1][k])