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
N, K = map(int, input().split())
*a, = map(int, input().split())
MOD = 10**9+7

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

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

    for j in range(1, K+1):
        sj = max([0, j-a[i-1]])
        dp[i][j] = (sums[j+1]-sums[sj]+MOD) % MOD

print(dp[N][K])
