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
#!/usr/bin/env python3

#import
#import math
#import numpy as np
N, K = map(int, input().split())
A = list(map(int, input().split()))
MOD = 10 ** 9 + 7

def mod(num):
    return num % MOD

dp = [[0] * (K + 1) for _ in range(N + 1)]
dp[0][0] = 1

for i in range(1, N + 1):
    s = [0] * (K + 2)
    for j in range(1, K + 2):
        s[j] = mod(s[j - 1] + dp[i - 1][j - 1])

    for j in range(K + 1):
        dp[i][j] =  mod(s[j + 1] - s[max(0, j - A[i-1])])

print(dp[N][K])

