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 <bits/stdc++.h>
#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define REPS(i,n) for(int i=1;i<=(int)(n);i++)
using namespace std;
using ll = long long;
using ld = long double;

int N, M, Q;
int a[50], b[50], c[50], d[50];
vector<int> buf;

int ans = 0;
void dfs(int i, const int size, const int range_start, const int range_end)
{
    if (i == size) {
        int sum = 0;
        vector<int> S;
        for(int i = 0; i < buf.size(); i++) {
            S.push_back(buf[i]);
        }
        for (int i = 0; i < Q; i++) {
            if (S[b[i]-1] - S[a[i]-1] == c[i]) {
                sum += d[i];
            }
            if (sum > ans) {
                ans = sum;
            }
        }
    }
    else{
        for(int j = range_start; j <= range_end; j++){
            buf[i] = j;
            dfs(i + 1, size, j, range_end);
        }
    }
}

int main(void) {
    cin >> N >> M >> Q;
    for (int i = 0; i < Q; i++) {
        cin >> a[i] >> b[i] >> c[i] >> d[i];
    }

    buf.resize(N);
    dfs(0, N, 1, M);
    cout << ans << endl;
}