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
import sys
def input(): return sys.stdin.readline().rstrip()
def main():
    n,k=map(int,input().split())
    A=list(map(int,input().split()))
    dp=[[0]*(k+1) for _ in range(n+1)]
    dp[0][0]=1
    cum=[0]*(k+2)
    mod=10**9+7
    for i in  range(1,n+1):
        cum[0]=0 #dp[i-1]のj未満の和
        for j in range(k+1):
            cum[j+1]=cum[j]+dp[i-1][j]
        for j in range(k+1):
            dp[i][j]=(cum[j+1]-cum[max(0,j-A[i-1])])%mod
    print(dp[n][k])
if __name__=='__main__':
    main()