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 = [0] + list(map(int, input().split()))
DP = [[0 for k in range(K+1)] for n in range(N+1)]
cs = [[0 for k in range(K+2)] for n in range(N+1)]
for i in range(1,N+1):
    for j in range(0,K+2):
        if i == 1 and j <= K:
            if j <= a[i]:
                DP[i][j] = 1
            else:
                DP[i][j] = 0
        elif j <= K:
            DP[i][j] += (cs[i-1][j+1] - cs[i-1][max(j-a[i],0)])%(10**9+7)
        if j > 0:
            cs[i][j] = (cs[i][j-1]%(10**9+7) + DP[i][j-1]%(10**9+7))%(10**9+7)
print(DP[N][K])