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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>

using namespace std;

int *num_array;
int array_len;
int num_max;
int score_len;

vector<int> as;
vector<int> bs;
vector<int> cs;
vector<int> ds;

bool array_next(int index);

int main(void)
{
    cin >> array_len >> num_max >> score_len;

    for(int i = 0; i < score_len; i++){
        int a, b, c, d;
        cin >> a >> b >> c >> d;
        as.push_back(a - 1);
        bs.push_back(b - 1);
        cs.push_back(c);
        ds.push_back(d);
    }

    num_array = new int[array_len];

    for(int i = 0; i < array_len; i++){
        num_array[i] = 1;
    }
    num_array[array_len - 1] = 0;

    int max_score = 0;
    while(array_next(array_len - 1)){
        bool ascend = true;
        for(int i = 0; i < array_len - 1; i++){
            if(num_array[i] > num_array[i + 1]){
                ascend = false;
                break;
            }
        }

        if(ascend){
            int current_sum = 0;
            for(int i = 0; i < score_len; i++){
                if(num_array[bs[i]] - num_array[as[i]] == cs[i]){
                    current_sum += ds[i];
                }
            }

            if(current_sum > max_score){
                max_score = current_sum;
            }
        }
    }

    cout << max_score << endl;

    return 0;
}

bool array_next(int index)
{
    if(num_array[index] == num_max){
        if(index == 0){
            return false;
        }
        bool cont = array_next(index - 1);
        if(cont){
            for(int i = index; i < array_len; i++){
                num_array[i] = num_array[i - 1];
            }
        }
        return cont;
    }

    num_array[index] += 1;
    return true;
}