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 = list(map(int, input().split()))
MOD = 10**9 + 7

dp = [[0] * (K + 1) for _ in range(N + 1)]  # dp[child][candy] 残りcandy個の場合の数
dp[0][K] = 1

for child in range(1, N + 1):
    sumDp = [0] * (K + 2)
    for i in range(1, K + 2)[:: -1]:
        sumDp[i - 1] += sumDp[i] + dp[child - 1][i - 1]

    for candy in range(K + 1):
        dp[child][candy] = (sumDp[candy] - sumDp[min(K, candy + A[child - 1]) + 1]) % MOD

print(dp[N][0] % MOD)