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.Collections.Generic;
using System.Text;

namespace AtTest.EducationalDP
{
    class M
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            int[] nk = ReadInts();
            int n = nk[0];
            int k = nk[1];
            int[] array = ReadInts();
            long[,] dp = new long[100, k+1];
            long mask = 1000000000 + 7;
            for (int i = 0; i <= Math.Min(array[0], k); i++) dp[0, i] = 1;
            for (int i = 1; i < n; i++)
            {
                long[] sums = new long[k+1];
                sums[0] = dp[i - 1, 0];
                for (int j = 1; j <= k; j++)
                {
                    sums[j] = sums[j - 1] + dp[i - 1, j];
                }
                for (int j = 0; j <= k; j++)
                {
                    int index = j - array[i] - 1;
                    dp[i, j] = sums[j];
                    if (index >= 0) dp[i, j] -= sums[index];
                    dp[i, j] %= mask;
                }
            }
            /*for (int i = 0; i < n; i++)
            {
                for (int j = 0; j <= k; j++)
                {
                    Console.Write(dp[i, j] + " ");
                }
                Console.WriteLine();
            }*/
            Console.WriteLine(dp[n - 1, k]);
        }

        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}