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
MOD = 10**9+7

N, K = map(int, input().split())
a = list(map(int, input().split()))

# i 番目までに j 枚使ったときの場合の数
dp = [[0]*(K+1) for _ in range(N+1)]
dp[0][0] = 1

upper = 0
for i in range(1, N+1):
    for j in range(1, K+1):
        dp[i-1][j] += dp[i-1][j-1]
    upper += a[i-1]
    for j in range(min(upper, K)+1):
        if j > a[i-1]:
            dp[i][j] = dp[i-1][j] - dp[i-1][j-a[i-1]-1]
        else:
            dp[i][j] = dp[i-1][j]
        dp[i][j] %= MOD

print((dp[N][K]+MOD)%MOD)