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()))
dp = [0] * (k + 1)
# dp[i] - the number of ways such that we used i candies so far
dp[0] = 1
for i in range(n):
    fake = [0] * (k + 1)
    for used in range(k, -1, -1):
        tmp = dp[used]
        L = used + 1
        R = used + min(a[i], k - used)
        if L <= R:
            fake[L] = (fake[L] + tmp) % MOD
            if R + 1 <= k:
                fake[R + 1] = (fake[R + 1] - tmp + MOD) % MOD
    prefix_sum = 0
    for j in range(k + 1):
        prefix_sum = (prefix_sum + fake[j]) % MOD
        dp[j] = (dp[j] + prefix_sum) % MOD
print(dp[k])