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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;

class M
{
	static void Main()
	{
		Func<int[]> read = () => Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
		var h = read();
		var a = read();
		int n = h[0], k = h[1];

		var dp = new long[n + 1, k + 1];
		for (int i = 0; i <= n; i++) dp[i, 0] = 1;
		for (int j = 0; j <= k; j++) dp[0, j] = 1;
		for (int i = 1; i <= n; i++)
			for (int j = 1; j <= k; j++)
				dp[i, j] = MInt(dp[i, j - 1] + dp[i - 1, j] - (j > a[i - 1] ? dp[i - 1, j - a[i - 1] - 1] : 0));
		Console.WriteLine(MInt(dp[n, k] - (k > 0 ? dp[n, k - 1] : 0)));
	}

	const int m = 1000000007;
	static long MInt(long x) => (x %= m) < 0 ? x + m : x;
}