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 = 1000000007

n, k = map(int, raw_input().split())
a = map(int, raw_input().split())

dp = [[0] * (k + 1) for _ in range(n + 1)]
dp[0][0] = 1
for i in range(1, n + 1):
    suma = 0
    l = 0
    r = 0
    for j in range(k + 1):
        if l < j - a[i - 1]:
            suma -= dp[i - 1][l]
            l += 1
        if r <= j:
            suma += dp[i - 1][r]
            r += 1
        suma %= MOD
        dp[i][j] += suma
        dp[i][j] %= MOD
print(dp[n][k])
