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
input = sys.stdin.readline

n,k=map(int, input().split()) 
a=list(map(int, input().split()))
mod=10**9+7
dp=[[0]*(k+1) for i in range(n+1)]

for i in range(n+1):
    dp[i][0]=1



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

print(dp[-1][-1]%mod)
    
    