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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

public class S
{

    private const long DP_INIT_MINUS1 = -1;
    private const double DP_INIT_DOUBLE_MINUS1 = -1.0;
	private const long MOD = 1000000007;


    //s
    private const int FIRST_WIN = 1;
    private const int SECOND_WIN = 0;

    private static long[,] dp;


    public static void Main()
	{
		/*
        var input = Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
        var N = input[0];
        var M = input[1];
        */

        var input = Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
        var N = input[0];
        var K = input[1];

        solver(N,K, Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse));
    }

    public static void solver(long N, long K, long[] candies){

        /*
            EDPC M Candies
            dp[N,K], K消費？   
            dp[N,K], N人目で合計K個のパターン？
            
            x人目で合計がy個になるのは・・・
            x-1人目で合計がy,y-1... y-Axまでの範囲が遷移してくる
            この遷移のために、累積和を取っておく必要はありそう
           
            飴を使い切らなきゃいけないから、回答は安心してdp[N,K]。
            。
         */

        dp = new long[N+1,K+1];
        var cSum = new long[N+1,K+1];
        long add;
        

        //for(int i = 1; i <= N; i++){
            for(int k = 0; k <= K; k++){
				if(candies[0] < k){
					if(k == 0){
						cSum[1,k] = 0;
						continue;
					}
					cSum[1,k] = cSum[1,k-1];
                    continue;
				}
                if(candies[0] == 0){
					if(k == 0){
						cSum[1,k] = 1;
						continue;
					}
                    cSum[1,k] = cSum[1,k-1];
                    continue;
                }
                dp[1,k] = 1; //K個取りのパターンは初回はすべて1
				if(k == 0){
					cSum[1,k] = 1;
					continue;
				}
                cSum[1,k] = cSum[1,k-1] + 1;
            }
        //}

        for(int i = 2; i <= N; i++){

            for(int k = 0; k <= K; k++){

                add = ((k - candies[i-1] > 0) ? 
                            cSum[i-1,k] - cSum[i-1,k-candies[i-1]-1]
                            :
                            cSum[i-1,k]
                        );

                dp[i,k] += add;
				dp[i,k] %= 1000000007;
				if(k == 0){
					cSum[i,k] = dp[i,k];
					continue;
				}
				cSum[i,k] = cSum[i,k-1] + dp[i,k];

            }
			/*
			for(int k = 0; k <= K; k++){
				Console.Write(cSum[i,k] + ",");
				
			}
			Console.WriteLine();
			*/

            
        }

        Console.WriteLine(dp[N,K]);
		/*
		for(int i = 1; i <=N; i++){
			for(int k = 0; k <= K; k++){
				Console.Write(dp[i,k] + ",");	
			}
			Console.WriteLine();
		}
		*/
	}
}