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
# dp[i][j]=(i人目までにj個配る場合の数)
mod=10**9+7
def main():
    n,k=map(int,input().split())
    a=list(map(int,input().split()))
    dp=[[0]*(k+1) for _ in range(n)]
    for i in range(a[0]+1):
        dp[0][i]=1
    for i in range(1,n):
        dp[i][0]=dp[i-1][0]
        for j in range(1,k+1):
            dp[i][j]=dp[i-1][j]+dp[i][j-1]
            if j-a[i]>0:
                dp[i][j]-=dp[i-1][j-a[i]-1]
            dp[i][j]%=mod
    print(dp[-1][-1])
    # for i in dp:
    #     print(i) 
main()     