Score : $100$ points

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.

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 $10^9 + 7$.

3 4
1 2 3

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.

1 10
9

0

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

2 0
0 0

1

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

• $(0, 0)$

4 100000
100000 100000 100000 100000

665683269

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