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;
using System.Linq;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program
{
	static void Main()
	{
		string[] input = Console.ReadLine().Split(' ');
		int n = int.Parse(input[0]);
		int k = int.Parse(input[1]);
    int[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);
		long mod = 1000000007;
    long[,] dp = new long[n+1,k+1];
    long[,] sums = new long[n+1,k+2];
    dp[0,0] = 1;
    for(int i = 1; i <= k+1; i++) sums[0,i] = 1;

    for(int i = 1; i <= n; i++)
    {
      for(int j = 0; j <= k; j++)
      {
        dp[i,j] = sums[i-1,j+1] - sums[i-1,Math.Max(0, j-nums[i-1])];
        dp[i,j] += mod*2;
        dp[i,j] %= mod;

        sums[i,j+1] = sums[i,j] + dp[i,j];
        sums[i,j+1] += mod*2;
        sums[i,j+1] %= mod;

        //Console.WriteLine(i+" "+j+" "+dp[i,j]+" "+sums[i,j]);
      }
    }

		Console.WriteLine(dp[n,k]);
	}
}