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;

typedef long long ll;
#define int ll
#define pb push_back
const int INF = 1e18, MOD = 1e9+7;

signed main(){

	ios_base::sync_with_stdio(false);
	cin.tie(0);

	int n,k;
	cin>>n>>k;
	int arr[n+1];
	for(int i=1;i<=n;i++)
		cin>>arr[i];

	vector<int> dp(k+1,1), next(k+1,0);
	for(int i=1;i<=n;i++){
		next[0]= 1;
		for(int j=1;j<=k;j++){
			int left = max(0ll, j-arr[i]);
			next[j] = (left == 0) ? dp[j]: dp[j] - dp[left-1];
			next[j] = (next[j] + next[j-1])%MOD;
		}
	
		for(int j=0;j<=k;j++)
			dp[j] = next[j];
	}


	if (k!= 0) cout<<(dp[k]-dp[k-1] + MOD)%MOD;
	else cout<<1;

	return 0;
}