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
##x_1+x_2+...+x_N=K, 0<=x_i<=a_i
N,K=list(map(int,input().strip().split(' ')))
A=list(map(int,input().strip().split(' ')))
dp=[[0] * (K+1)  for i in range(N)]
for i in range(min(A[0]+1,K+1)):
    dp[0][i]=1
for i in range(N):
    dp[i][0]=1
MOD=10**9+7
for i in range(1,N):
    pre=[]
    temp=0
    for j in range(K+1):
        temp+=dp[i-1][j]
        temp%=MOD
        pre+=[temp]
        
    for j in range(1,K+1):
        ## j-A[i],j-(A[i]-1),...,j
        ## pre[j]-pre[j-A[i]-1]
        temp=0
        if j-A[i]>0:
            temp=pre[j-A[i]-1]
        dp[i][j]=pre[j]-temp
        dp[i][j]%=MOD

print(dp[-1][K])
        
        


