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()))

if K == 0:
    print (1)
    exit()

dp = [[0] * (K + 1) for _ in range(N + 1)]
for j in range(K + 1):
    dp[N][j] = 1
# dp[N][0] = 1
# print (dp[N])
for i in range(N - 1, -1, -1):
    for j in range(K + 1):
        if j <= A[i]:
            dp[i][j] = dp[i + 1][j]
        else:
            dp[i][j] = dp[i + 1][j] - dp[i + 1][j - A[i] - 1]
    # print (i)
    # print (dp[i])
    for j in range(K):
        dp[i][j + 1] += dp[i][j]
        dp[i][j + 1] %= MOD
    # print (dp[i])
    
print ((dp[0][K] - dp[0][K - 1]) % MOD)