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;

#define int long long
const int MOD = 1000000007LL;

signed main(){

    int n, k; cin >> n >> k;
    vector<vector<int> > dp(n + 1, vector<int> (3 * k + 1, 0LL));
    vector<int> a(n);
    for(int i = 0; i < n; i++) cin >> a[i];
    dp[0][0] = 1LL;

    for(int i = 0; i < n; i++){
        for(int j = 0; j <= k; j++){

            dp[i + 1][j] += dp[i][j];
            dp[i + 1][j] %= MOD;            
            dp[i + 1][j + a[i] + 1] -= dp[i][j];
            dp[i + 1][j + a[i] + 1] = (dp[i + 1][j + a[i] + 1] + MOD) % MOD;            

        }

        for(int j = 1; j <= 2*k; j++){
            dp[i + 1][j] += dp[i + 1][j - 1];
            dp[i + 1][j] %= MOD;            
        }
    }

    cout << dp[n][k] % MOD << endl;
    return 0;
}