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()))
d=[[0]*(K+2) for i in range(N+1)]
d[0]=[0]+[1]*(K+1)
m=10**9+7
for i in range(N):
    for j in range(K+1):
        d[i+1][j+1]=(d[i][j+1]-d[i][max(0,j-A[i])]+d[i+1][j])%m
print((d[-1][-1]-d[-1][-2])%m)