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: Runtime Error)

#include<iostream>
#include<vector>
using namespace std;
int n,m,q;
vector<long long> a,b,c,d;
long long score(const vector<int> &a){
long long res=0;
  for(int i=0;i<q;++i) if(a[b[i]]-a[a[i]]==c[i]) res+=d[i];
  return res;
}

long long dfs(vector<int> &Q){
  if(Q.size()==n){
    return score(Q);
  }
  long long res=0;
  int prev_last=(Q.empty()?0:Q.back());
  for(int add=prev_last;add<m;++add){
    Q.push_back(add);
    res=max(res,dfs(Q));
    Q.pop_back();
  }
  return res;
}
int main(){
 cin>>n>>m>>q;
  a.resize(q);b.resize(q);c.resize(q);d.resize(q);
  for(int i=0;i<q;i++){
    cin>>a[i]>>b[i]>>c[i]>>d[i];
    --a[q],--b[q];
  }
  vector<int>Q;
  cout<<dfs(Q)<<endl;
}