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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO.Pipes;
using System.Linq;
using System.Numerics;
using System.Security.Cryptography;
using System.Text;
using System.Threading;

namespace ForATCODER
{
    public class Program
    {
        public static void Main(string[] args)
        {

            int[] d = s2iarray(Console.ReadLine().Split(' '));
            int[] A = new int[d[2]];
            int[] B = new int[d[2]];
            int[] C = new int[d[2]];
            int[] D = new int[d[2]];
            int[] a = new int[d[0]];
            ulong scorem = 0;
            int p =a.Length-1;
            bool nc = false;
            for (int j = 0; j < a.Length; j++)

            {
                a[j] = 1;

            }
          a[a.Length-1] = a[a.Length - 1]-1;
                for (int i = 0; i < d[2]; i++)
            {
                int[] tmp = s2iarray(Console.ReadLine().Split(' '));
                A[i] = tmp[0];
                B[i] = tmp[1];
                C[i] = tmp[2];
                D[i] = tmp[3];
            }
            while (true)
            {
                if (a[0] == d[1]) break;
                bool b = false;
                int cp = -1;
                for (int i = a.Length-1; i >= 1; i--)
                {
                   if( a[i]-a[i-1]>=1) { b = true; cp = i - 1;  }
                }
                if(cp>=0) a[cp]++;

                if (!b)
                {
                    if (a[p] <= d[1] - 1) a[p]++;
                    else { p--;
                        
                        a[p]++; };

                    for (int j = 0; j < p; j++)
                    {
                        a[j] = 1;
                    }
                }
                /*    if (a[a.Length - 1] > d[1])
                    {
                        for (int j = a.Length - 1; j >= 1; j--)
                        {

                                if (a[j - 1] + 1 >= a[j]) continue;
                                a[j - 1]++;
                            a[a.Length - 1] = d[1];
                                break;

                        }
                    }*/
#if DEBUG
                Console.WriteLine("[{0}]", string.Join(", ", a));
#endif
                //得点
                ulong score = 0;
                for (int i = 0; i < d[2]; i++)
                {
                    int c = a[B[i] - 1] - a[A[i] - 1];
                    int c_ = C[i];
                    if (c == c_)
                    {
                        score += (ulong)D[i];
                  //      RESULT(score);
                    }
                }
                if (scorem < score) scorem = score;
                nc = false;

            }
            for (int j = 0; j < a.Length; j++)

            {
                a[j] = 1;

            }
            p = a.Length - 1;
            while (true)
            {
                if (a[0] == d[1]) break;
                bool b = false;
                int cp = -1;
                for (int i = a.Length - 1; i >= 1; i--)
                {
                    if (a[i] - a[i - 1] >= 1) { b = true; cp = i - 1;break; }
                }
                if (cp >= 0) a[cp]++;

                if (!b)
                {
                    if (a[p] <= d[1] - 1) a[p]++;
                    else
                    {
                        p--;

                        a[p]++;
                    };

                    for (int j = 0; j < p; j++)
                    {
                        a[j] = 1;
                    }
                }
                /*    if (a[a.Length - 1] > d[1])
                    {
                        for (int j = a.Length - 1; j >= 1; j--)
                        {

                                if (a[j - 1] + 1 >= a[j]) continue;
                                a[j - 1]++;
                            a[a.Length - 1] = d[1];
                                break;

                        }
                    }*/
#if DEBUG
                Console.WriteLine("[{0}]", string.Join(", ", a));
#endif
                //得点
                ulong score = 0;
                for (int i = 0; i < d[2]; i++)
                {
                    int c = a[B[i] - 1] - a[A[i] - 1];
                    int c_ = C[i];
                    if (c == c_)
                    {
                        score += (ulong)D[i];
                        //      RESULT(score);
                    }
                }
                if (scorem < score) scorem = score;
                nc = false;

            }

            RESULT(scorem);

        }
        
        public static ulong pow(int a, int b)
        {
            ulong res = 1;
            for (int i = 0; i < b; i++)
            {
                res *= (ulong)a;
            }
            return res;
        }
        public static void sortT<T>(T[] arr, int index)
        {

            // If the index is negative,  
            // it represents the bitwise 
            // complement of the next larger  
            // element in the array. 
            if (index < 0)
            {

                index = ~index;

                if (index == 0)
                    Console.Write("beginning of array");
                else
                    Console.Write("{0} and ", arr[index - 1]);

                if (index == arr.Length)
                    Console.WriteLine("end of array.");
                else
                    Console.WriteLine("{0}", arr[index]);
            }
        }







        static int s2i(String s)
        {
            return Convert.ToInt32(s);
        }
        static ulong s2l(String s)
        {
            return Convert.ToUInt64(s);
        }
        static void RESULT(double res)
        {
            Console.WriteLine(res);
        }
        static void RESULT(long res)
        {
            Console.WriteLine(res);
        }
        static void RESULT(ulong res)
        {
            Console.WriteLine(res);
        }
        static void RESULT(int res)
        {
            Console.WriteLine(res);
        }
        static void RESULT(String res)
        {
            Console.WriteLine(res);
        }
        static String[] ReadLineAll(int count)
        {
            String[] res = new String[count];
            for (int i = 0; i < count; i++)
            {
                res[i] = Console.ReadLine();
            }
            return res;
        }

        static int[] s2iarray(String[] src)
        {
            int len = src.Length;
            int[] res = new int[len];
            for (int i = 0; i < len; i++)
            {
                res[i] = Convert.ToInt32(src[i]);
            }
            return res;
        }
        static long[] s2larray(String[] src)
        {
            int len = src.Length;
            long[] res = new long[len];
            for (int i = 0; i < len; i++)
            {
                res[i] = Convert.ToInt64(src[i]);
            }
            return res;
        }
        static ulong[] s2larray2(String[] src)
        {
            int len = src.Length;
            ulong[] res = new ulong[len];
            for (int i = 0; i < len; i++)
            {
                res[i] = Convert.ToUInt64(src[i]);
            }
            return res;
        }
    }
}