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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

const int MAXN = 55;
int a[MAXN], b[MAXN], c[MAXN], d[MAXN];

int n, m, q;
vector<int> vec;

int ans = 0;

void solve(int x, int y) {
    if (x == n + 1) {
        int cur = 0;
        for (int i = 1; i <= n; i++) {
            if (vec[b[i]] - vec[a[i]] == c[i]) {
                cur += d[i];
            }
        }
        ans = max(ans, cur);
    } else {
        for (int i = y; i <= m; i++) {
            vec.push_back(i);
            solve(x + 1, i);
            vec.pop_back();
        }
    }
}

int main() {
    scanf("%d%d%d", &n, &m, &q);// don't forget &
    for (int i = 1; i <= q; i++) {
        scanf("%d%d%d%d", &a[i], &b[i], &c[i], &d[i]);// don't forget &
    }
    vec.push_back(0);
    solve(1, 1);
    printf("%d", ans);
    return 0;
}