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 for i in range(0,K+1)] for i in range(0,N)]
for i in range(0,K+1):
    if A[0]>=i:
        dp[0][i]=1

for i in range(1,N):
    for j in range(0,K+1):
        if j==0:
            dp[i][j]=dp[i-1][j]
        elif A[i]>=j:
            dp[i][j]=(dp[i][j-1]+dp[i-1][j])%mod
        else:
            dp[i][j]=(dp[i][j-1]+dp[i-1][j]-dp[i-1][j-1-A[i]])%mod

print(dp[N-1][K])