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
input = sys.stdin.buffer.readline

def main():
    N,K = map(int,input().split())
    a = list(map(int,input().split()))
    MOD = 10**9+7
    
    dp = [0 for _ in range(K+2)]
    dp[0] = 1
    for num in a:
        imos = [0 for _ in range(K+2)]
        for i in range(K+2):
            imos[i] += dp[i]
            imos[min(K+1,i+num+1)] -= dp[i]
        for i in range(K+1):
            imos[i+1] += imos[i]
            imos[i+1] %= MOD
        dp = imos
        
    print(dp[K])
        
if __name__ == "__main__":
    main()
