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>
using namespace std;
typedef long long int ll;
ll mod = 1000000007;

ll r(ll x, ll y) {
  if (y == 0) return 1;
  else if (y % 2 == 0) return r(x, y/2) * r(x, y/2) % mod;
  else return x * r(x, (y-1)/2) % mod * r(x, (y-1)/2) % mod;
}

int n, m, q;
ll ans;
vector<int> a, b, c, d;
void dfs(vector<int> A) {
  if (A.size() == n+1) {
    ll sum = 0;
    for (int i = 0; i < q; i++) {
      if (A[b[i]] - A[a[i]] == c[i]) sum += d[i];
    }
    ans = max(ans, sum);
    return;
  }
  
  A.push_back(A.back());
  while (A.back() <= m) {
    dfs(A);
    A.back()++;
  }
}


int main() {
  cin >> n >> m >> q;
  a = b = c = d = vector<int>(q);
  for (int i = 0; i < q; i++) {
    cin >> a[i] >> b[i] >> c[i] >> d[i];
  }
  dfs(vector<int> (1, 1));
  cout << ans <<endl;
}