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()))
mod=10**9+7
dp=[[0]*(k+1) for _ in range(n+1)]
dp[0][0]=1
for i in range(1,n+1):
    accum=[0,dp[i-1][0]]
    for j in range(1,k+1):
        accum.append((dp[i-1][j]+accum[-1])%mod)
    for j in range(k+1):
        dp[i][j]+=(accum[j+1]-accum[max(j-a[i-1],0)]+mod)%mod
        dp[i][j]%=mod
print(dp[n][k])