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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;

namespace AtCoder.DP
{
    class EDPC_M
    {
        public static void Main()
        {
            var nk = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            var a = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            var n = nk[0];
            var k = nk[1];

            const long mod = 1000000007;
             
            var dp = new long[n + 1, k + 1];

            var acc = 0;
            for (int i = 1; i <= n; i++)
            {
                acc += a[i - 1];
                dp[i, 0] = 1;
                for (int j = 1; j <= Math.Min(acc, k); j++)
                {
                    dp[i, j] = dp[i - 1, j] + dp[i, j - 1];
                    if (j > a[i - 1])
                        dp[i, j] -= dp[i - 1, j - 1 - a[i - 1]];
                    dp[i, j] %= mod;
                }
            }
            Console.WriteLine(dp[n, k] < 0 ? dp[n, k] + mod : dp[n, k]);
        }
    }
}