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.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static public int[] Sarray() { return ReadLine().Split().Select(int.Parse).ToArray(); }
        static public List<int> Slist() { return ReadLine().Split().Select(int.Parse).ToList(); }

        static int[] A;
        static long[,] dp;
        static readonly long Mod = 1000000000 + 7;
        static void Main(string[] args)
        {
            var NK = Sarray();
            var N = NK[0];
            var K = NK[1];
            A = Sarray();
            var amax = A.Max();
            if(A.Sum()<K)
            {
                WriteLine(0);
                return;
            }
            dp = new long[N, K + 1];
            for (var i = 1; i < N; ++i)
                dp[i, 0] = 1;
            for (var i = 0; i <= A[0]; ++i)
                dp[0, i] = 1;
            var sum = A[0];
            for (var i = 1; i < N; ++i)
            {
                sum = Min(sum + A[i], K);
                for (var j = 1; j <= sum; ++j)
                {
                    dp[i, j] = dp[i - 1, j] + dp[i, j - 1];
                    if (0 < j - A[i])
                        dp[i, j] -= dp[i - 1, j - A[i] - 1];
                    dp[i, j] %= Mod;
                }
            }
            WriteLine(dp[N - 1, K]);
        }
    }
}