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: Time Limit Exceeded)

#include <bits/stdc++.h>

using namespace std;

#define ll long long
#define mod 1000000007
#define inf 100005
ll *a, n;
ll dp[101][inf];

ll ways(ll i, ll left){
	//base case
	if(i==n){return left==0;}
	if(left==0){return 1;}

	//recursive case
	if(dp[i][left]!=-1){return dp[i][left];}

	dp[i][left]=0;
	for(ll j=0; j<=a[i]&&j<=left; j++){
		dp[i][left] += ways(i+1, left-j);
		dp[i][left] %= mod;
	}
	return dp[i][left];
}

int main(){
	ios_base::sync_with_stdio(false);
    cin.tie(NULL);
	memset(dp, -1, sizeof(dp));
	ll k;
	cin>>n>>k;
	a = new ll[n];
	for(int i=0; i<n; i++){
		cin>>a[i];
	}
	cout<<ways(0, k);
	
}