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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
const int mod=1e9+7;
const int maxn=1e5+10;
const int maxm=110;
long long int dp[maxm][maxn];
int n;
int k;
int a[maxm];
int main(){
	ios_base::sync_with_stdio(false),cin.tie(0),cout.tie(0);
     cin>>n>>k;
     for(int i=1;i<=n;i++){
     	cin>>a[i];
	 }
	 dp[0][0]=1;
	 for(int i=1;i<=k;i++){
	 	dp[0][i]+=dp[0][i-1];
	 }
	 for(int i=1;i<=n;i++){
	 	for(int j=0;j<=k;j++){
	 		if(a[i]>=j){
	 			dp[i][j]=dp[i-1][j];
			 }
			 else{
	 		dp[i][j]=((dp[i-1][j]-dp[i-1][j-a[i]-1])+mod)%mod;
	 	}
	 	if(j>0&&i!=n){
	 	dp[i][j]+=dp[i][j-1];
	 dp[i][j]%=mod;
	 }
		 }

	 }
	 cout<<dp[n][k];
	 }