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
# coding: utf-8
# Your code here!
MOD=10**9+7

n,k = [int(i) for i in input().split()]
aa = [int(i) for i in input().split()]

dp=[0]*(2*k+1)
dp[0]=1
for a in aa:
    l=k-a
    s=sum(dp[l:k+1])%MOD
    for i in range(k,-1,-1):
#        print(s,i,l)
        s-=dp[i]
        s%=MOD
        dp[i] += s
        l-=1
        s+=dp[l]
#    print(dp)
        
    
print(dp[k]%MOD)
