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
import sys
INF = 10 ** 15
MOD = 10 ** 9 + 7
sys.setrecursionlimit(100000000)
input = sys.stdin.readline
from math import pi
from functools import lru_cache

def main():
    n,k = map(int,input().split())
    a = list(map(int,input().split()))
    dp = [[0,1] + [0] * k for _ in range(n + 1)]

    for i in range(n):
        m = a[i]
        for j in range(k + 1):
            dp[i][j + 1] += dp[i][j]
            dp[i][j + 1] %= MOD
        for j in range(1,k + 1):
            dp[i + 1][j + 1] = dp[i][j + 1] - dp[i][max(j - m,0)]
            dp[i + 1][j + 1] %= MOD
    
    print(dp[-1][-1])

if __name__ =='__main__':
    main()    