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

NOW=[0]*(K+1)
NOW[0]=1#そこまでi個使ったときの場合の数


for i in range(N):
    NEXT=[0]*(K+1)
    NOWSUM=[0]
    for n in NOW:
        NOWSUM.append(NOWSUM[-1]+n)
        
    for j in range(K+1):
        NEXT[j]=(NEXT[j]+NOWSUM[j+1]-NOWSUM[max(0,j-A[i])])%mod

    NOW=NEXT
    #print(NOWSUM,NOW)

print(NOW[K])