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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public final class Main {

    public static void main(String[] args) {
        final Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        final int n = in.nextInt();
        final int m = in.nextInt();
        final int q = in.nextInt();
        in.nextLine();
        final int[][] lines = new int[q][4];
        for (int i = 0; i < q; i++) {
            lines[i] = new int[] { in.nextInt(), in.nextInt(), in.nextInt(), in.nextInt() };
            in.nextLine();
        }
        int res = 0;
        for (List<Integer> l : combine(m, n)) {
            int curr = 0;
            for (int[] query : lines) {
                if (l.get(query[1] - 1) - l.get(query[0] - 1) == query[2]) {
                    curr += query[3];
                }
            }
            res = Math.max(res, curr);
        }
        System.out.println(res);
    }

    public static List<List<Integer>> combine(int n, int k) {
        final List<List<Integer>> res = new ArrayList<>();
        recurse(1, n, k, new ArrayList<>(), res);
        return res;
    }

    public static void recurse(int start, int n, int k, List<Integer> curr, List<List<Integer>> res) {
        if (k == 0) {
            res.add(new ArrayList<>(curr));
            return;
        }

        for (int i = start; i <= n - k + 1; i++) {
            curr.add(i);
            recurse(i, n, k - 1, curr, res);
            curr.remove(curr.size() - 1);
        }
    }
}