Problem:
Score : 300 points

Problem Statement

Given are positive integers N, M, Q, and Q quadruples of integers ( a_i , b_i , c_i , d_i ).

Consider a sequence A satisfying the following conditions:

A is a sequence of N positive integers.

1 \leq A_1 \leq A_2 \le \cdots \leq A_N \leq M.

Let us define a score of this sequence as follows:

The score is the sum of d_i over all indices i such that A_{b_i} - A_{a_i} = c_i. (If there is no such i, the score is 0.)

Find the maximum possible score of A.

Constraints

All values in input are integers.

2 ≤ N ≤ 10

1 \leq M \leq 10

1 \leq Q \leq 50

1 \leq a_i < b_i \leq N ( i = 1, 2, ..., Q )

0 \leq c_i \leq M - 1 ( i = 1, 2, ..., Q )

(a_i, b_i, c_i) \neq (a_j, b_j, c_j) (where i \neq j)

1 \leq d_i \leq 10^5 ( i = 1, 2, ..., Q )

Input

Input is given from Standard Input in the following format:

N M Q
a_1 b_1 c_1 d_1
:
a_Q b_Q c_Q d_Q

Output

Print the maximum possible score of A.

Sample Input 1

3 4 3
1 3 3 100
1 2 2 10
2 3 2 10

Sample Output 1

110

When A = \{1, 3, 4\}, its score is 110. Under these conditions, no sequence has a score greater than 110, so the answer is 110.

Sample Input 2

4 6 10
2 4 1 86568
1 4 0 90629
2 3 0 90310
3 4 1 29211
3 4 3 78537
3 4 2 8580
1 2 1 96263
1 4 2 2156
1 2 0 94325
1 4 3 94328

Sample Output 2

357500

Sample Input 3

10 10 1
1 10 9 1

Sample Output 3

1

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

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

namespace AtCoderCs
{

    class Program
    {

        const int Mod = 1000000007;

        static void Main()
        {

            var arg = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            var num = arg[0];
            var max = arg[1];
            var quest = new List<int[]>[num];

            for (int i = 0; i < num; i++) quest[i] = new List<int[]>();

            for (int i = 0; i < arg[2]; i++)
            {

                var buf = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
                quest[buf[1] - 1].Add(buf);

            }

            var result = 0;
            var bufs = new int[num];

            Solve(0, 0);

            Console.WriteLine(result);

            void Solve(int Gen, int Sum)
            {

                if (Gen == num - 1)
                {

                    for (bufs[Gen] = (Gen == 0 ? 1 : bufs[Gen - 1]); bufs[Gen] <= max; bufs[Gen]++)
                    {

                        var buffer = Sum + quest[Gen].Where(x => bufs[Gen] - bufs[x[0] - 1] == x[2]).Sum(x => x[3]);
                        if (result < buffer) result = buffer;

                    }

                }
                else
                {

                    for (bufs[Gen] = (Gen == 0 ? 1 : bufs[Gen - 1]); bufs[Gen] <= max; bufs[Gen]++)
                    {

                        Solve(Gen + 1, Sum + quest[Gen].Where(x => bufs[Gen] - bufs[x[0] - 1] == x[2]).Sum(x => x[3]));

                    }

                }

            }

        }


    }
}