p03172 Educational DP Contest - Candies
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
```python
mod = 10**9+7

def comb(a,b):
      return fact[a]*inv[b]*inv[a-b]%mod
  
n,k = map(int, input().split())
a = list(map(int, input().split()))
fact = [1]
for i in range(n+k):
    fact.append(fact[-1]*(i+1)%mod)
inv = [1]*(n+k+1)
inv[n+k] = pow(fact[n+k],mod-2,mod)
for i in range(n+k)[::-1]:
    inv[i] = inv[i+1]*(i+1)%mod
f = [comb(i+n-1,n-1) for i in range(k+1)]
for i in a:
    for j in range(k-i)[::-1]:
        f[j+i+1] -= f[j]
        f[j+i+1] %= mod
print(f[k])
```