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 = [0]*110
a[1:] = list(map(int,input().split()))
MOD = 10**9+7
dp = [[0]*110000 for _ in range(110)]
dp_sum = [[0]*110000 for _ in range(110)]
dp[0][0] = 1
for i in range(K+1):
    dp_sum[0][i] = 1

for i in range(1,N+1):
    for j in range(K+1):
        dp[i][j] = dp_sum[i-1][j]
        if j - a[i]-1 >= 0:
            dp[i][j] -= dp_sum[i-1][j-a[i]-1]

        if j-1 >= 0:
            dp_sum[i][j] = dp_sum[i][j-1] + dp[i][j]
        else:
            dp_sum[i][j] = dp[i][j]
        dp[i][j] %= MOD
        dp_sum[i][j] %= MOD
print(dp[N][K])
# for i in range(N+1):
#     print(dp[i])