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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;


typedef long long ll;

const ll mdl = 1e9 + 7;



int main() {

	ll n, k;
	cin >> n >> k;

	ll ans[n + 1][k + 1];
	ll a[n];
	for (int i = 0; i < n; i++) cin >> a[i];
	for (int i = 0; i <= k; i++) {
		ans[1][i] = (i <= a[0]) ? 1 : 0;
	}

	for (int i = 2; i <= n; i++) {
		for (int j = 0; j <= k; j++) {
			if (j == 0)
				ans[i][j] = ans[i - 1][j];
			else {
				ans[i][j] = ans[i][j - 1] + ans[i - 1][j];
				if (j - 1 - a[i - 1] >= 0)
					ans[i][j] -= ans[i - 1][j - 1 - a[i - 1]];
			}
			ans[i][j] = ans[i][j] % mdl;

		}
	}

	cout << (ans[n][k] % mdl) << endl;

	return 0;

}