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
from sys import stdin
from itertools import accumulate
input = stdin.readline

MOD = 10**9+7
N, K = map(int,input().split())
a = list(map(int,input().split()))

p = list(accumulate(a))

dp = [0] * (K+1)
dp[0] = 1
prefix = [0]+[1]*(K+1)
for i in range(N):
    new_dp = [0]*(K+1)
    for j in range(min(p[i],K)+1):
        new_dp[j] = prefix[j+1] - prefix[max(0,j-a[i])]
    dp = new_dp[:]
    prefix = [i % MOD for i in [0]+list(accumulate(dp))]

print(dp[K]%MOD)
