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 itertools import accumulate

MOD = 10**9 + 7
N, K = map(int, input().split())
*A, = map(int, input().split())
dp = [0] * (K+1)
dp[K] = 1
for a in A:
    temp = [0] * (K+1)
    for k in range(K+1):
        temp[k - min(a, k)] += dp[k]; temp[k - min(a, k)] %= MOD
        temp[k] -= dp[k]; temp[k] %= MOD
    temp = list(accumulate(temp))
    dp = [(d + t) % MOD for d, t in zip(dp, temp)]
print(dp[0] % MOD)