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 (1.14.1) (judge verdict: Wrong Answer)

package main

import "fmt"
var N, K int
var u, w, v int
var dp, arr []int
var DP, mat [][]int
var vis, dist []int

const (
	MaxInt = 1<<31 - 1
	MinInt = -MaxInt - 1
	MOD = int(1e9) + 7
)
func addSelf(a *int, b int) {
	*a += b
}

func subSelf(a *int, b int) {
	*a -= b
}

func addSelfMOD(a *int, b int) {
	addSelf(a, b)
	if *a > MOD {
		*a -= MOD
	}
}

func subSelfMOD(a *int, b int) {
	subSelf(a, b)
	if *a < 0 {
		*a += MOD
	}
}
func max(a, b int) int {
	if a > b { return a }
	return b
}

func min(a, b int) int {
	if a < b { return a }
	return b
}

func abs(a int) int {
	if a < 0 { return -a }
	return a
}

func main() {
	_,e := fmt.Scanf("%d%d", &N, &K)
	if e != nil { return }
	dp = make([]int, K+1)
	dp[0] = 1
	for i:=0; i<N; i++ {
		_,e = fmt.Scanf("%d", &u)
		if e != nil { return }
		fake := make([]int, K+1)
		for used:=K; used>=0; used-- {
			tmp, L,R := dp[used], used+1, used + min(u, K-used)
			if L<=R {
				addSelfMOD(&fake[L], tmp)
				if R+1 <= K {
					subSelf(&fake[R+1], tmp)
				}
			}
		}
		prefix := 0
		for i := range fake {
			addSelfMOD(&prefix, fake[i])
			addSelfMOD(&dp[i], prefix)
		}
	}
	fmt.Println(dp[K])
}