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

def solve():
    input = sys.stdin.readline
    N, K = map(int, input().split())
    A = [int(a) for a in input().split()]
    mod = 7 + 10 ** 9
    DP = [[0 for j in range(K + 1)] for i in range(N)]
    for i in range(A[0] + 1): DP[0][i] = 1
    cum = [0] * (K + 2)
    for i in range(1, N):
        for j in range(1, K + 2): cum[j] = (cum[j-1] + DP[i-1][j-1]) % mod
        for j in range(K + 1): DP[i][j] = (cum[j + 1] - cum[max(0, j - A[i])]) % mod
    print(DP[N-1][K])

    return 0

if __name__ == "__main__":
    solve()