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;

int n,m,q;
vector<int>sum,ans,a,b,c,d;

void dfs(int cnt){
    if(cnt==n-1){
        int S=0;
        for(int i=0;i<q;++i){
            if(sum[b[i]]-sum[a[i]]==c[i])S+=d[i];
        }
        ans.push_back(S);
    }
    else if(cnt<n){
        for(int i=0;i<m-sum[cnt];++i){
            sum[cnt+1]=sum[cnt]+i;
            dfs(cnt+1);
        }
    }
}

int main(){
    cin>>n>>m>>q;
    sum.resize(n,0);
    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[i]--;b[i]--;
    }
    dfs(0);
    sort(ans.begin(),ans.end());
    reverse(ans.begin(),ans.end());
    cout<<ans[0]<<endl;
}