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

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