Contest Duration: ~ (local time)
M - Candies

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

N 人の子供たちがいます。 子供たちには 1, 2, \ldots, N と番号が振られています。

### 制約

• 入力はすべて整数である。
• 1 \leq N \leq 100
• 0 \leq K \leq 10^5
• 0 \leq a_i \leq K

### 入力

N K
a_1 a_2 \ldots a_N


### 入力例 1

3 4
1 2 3


### 出力例 1

5


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

### 入力例 2

1 10
9


### 出力例 2

0


### 入力例 3

2 0
0 0


### 出力例 3

1


• (0, 0)

### 入力例 4

4 100000
100000 100000 100000 100000


### 出力例 4

665683269


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.

### 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.