Problem Statement

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.

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.

Constraints

• All values in input are integers.
• $1 \leq N \leq 100$
• $0 \leq K \leq 10^5$
• $0 \leq a_i \leq K$

Sample Input 1

3 4
1 2 3

Sample Output 1

5

There are five ways for the children to share candies, as follows:

• (0, 1, 3)
• (0, 2, 2)
• (1, 0, 3)
• (1, 1, 2)
• (1, 2, 1)

Here, in each sequence, the i-th element represents the number of candies that Child i receives.

Sample Input 2

1 10
9

Sample Output 2

0

There may be no ways for the children to share candies.

Sample Input 3

2 0
0 0

Sample Output 3

1

There is one way for the children to share candies, as follows:

• (0, 0)

Sample Input 4

4 100000
100000 100000 100000 100000

Sample Output 4

665683269

Be sure to print the answer modulo 10^9 + 7.

见题面 Input 部分

见题面 Output 部分