Problem:
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.

Solution in Go (1.6) (judge verdict: Wrong Answer)

package main

import "fmt"

var CYCLE = 1000000007
var N, K int
var a [100]int
var results [100][100001]int

func max(a int, b int) int {
	if a > b {
		return a
	} else {
		return b
	}
}

func main() {
	fmt.Scan(&N, &K)
	for i := 0; i < N; i++ {
		fmt.Scan(&a[i])
	}

	for j := 0; j <= a[N-1] && j <= K; j++ {
		results[N-1][j] = 1
	}

	for i := N - 2; i >= 0; i-- {
		for j := 0; j <= K; j++ {
			r := results[i+1][j]
			if j > 0 {
				r += results[i][j-1]
			}
			if j-1-a[i] >= 0 {
				r -= results[i+1][j-1-a[i]]
			}
			results[i][j] = r % CYCLE
		}
	}

	fmt.Println(results[0][K])

	// for i := 0; i < N; i++ {
	// 	fmt.Println(results[i][:K+1])
	// }
}