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
mod=10**9+7
N,K=map(int,input().split())
a = list(map(int,input().split()))
ans=[[0 for e in range(K+1)] for f in range(N+1)]
for e in range(K+1):
 ans[1][e]=min(e+1,a[0]+1)
if N>1:
 for i in range(2,N+1):
  ans[i][0]=1
  for j in range(1,K+1):
   ans[i][j]=ans[i][j-1]+ans[i-1][j]
   if j-a[i-1]-1>=0:
    ans[i][j]-=ans[i-1][j-a[i-1]-1]
   ans[i][j]%=mod
if K==0:
 print(ans[N][K])
else:
 print((ans[N][K]-ans[N][K-1])%mod)
    