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>
#include <stdlib.h>
#include <iostream>
#include <math.h>
#include <algorithm>
#include <string>
#include <string.h>
#include <vector>
#include <functional>
#include <queue>
#include <unordered_set>
#include <climits>

using namespace std;
typedef long long ll;

ll N, M, Q;
ll a[51];
ll b[51];
ll c[51];
ll d[51];

ll ans = 0;

void Recursive(int level, int m, int a_[]){
	if(level == N){
		a_[N] = a_[level-1] + m;
		
		ll sum = 0;
		for(int i = 1; i <= Q; i++){
			if(a_[b[i]]-a_[a[i]] == c[i]){
				sum += d[i];
			}
		}
		ans = max(ans, sum);
		
		/*
		for(int i = 1; i <= N; i++){
			cout << a[i] << " ";
		}
		cout << sum << endl;
		*/
	}
	else{
		for(int i = 0; i <= m; i++){
			int aa[20];
			for(int j = 0; j < N; j++){
				aa[j] = a_[j];
			}
			aa[level+1] = a_[level] + i;
			Recursive(level+1, m-i, aa);
		}
	}
}

int main()
{
	cin >> N >> M >> Q;
	for(int i = 1; i <= Q; i++){
		cin >> a[i] >> b[i] >> c[i] >> d[i];
	}
	int A[20];
	for(int i = 0; i < N; i++){
		A[i] = 1;
	}
	Recursive(1, M-1, A);
	
	cout << ans << endl;
	
	return 0;
}