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 <stdio.h>

int main(void){

  int n,m,q;
  scanf("%d %d %d", &n, &m, &q);
  int a[q],b[q],c[q];
  long d[q];
  for (long i = 0; i < q; i++) {
    scanf("%d %d %d %ld", &a[i], &b[i], &c[i], &d[i]);
  }
  long max = 0;
  long score;
  int sequence[n];
  for (int i = 0; i < n; i++) {
    sequence[i] = 1;
  }
  while (1) {
    score = 0;
    for (int i = 0; i < q; i++) {
      if (sequence[b[i]-1]-sequence[a[i]-1] == c[i]) {
        score += d[i];
      }
    }
    if (score > max) {
      max = score;
    }
    if (sequence[1] == m) {
      break;
    }
    for (int i = n-1; i > 0; i--) {
      if (sequence[i] < m) {
        sequence[i]++;
        for (int j = i+1; j < n; j++) {
          sequence[j] = sequence[i];
        }
        break;
      }
    }
  }
  printf("%ld\n", max);

  return 0;
}