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"
#define ll long long
#define mk make_pair
#define pb push_back
#define pii pair<int,int>
#define pll pair<ll,ll>
#define pil pair<int,ll>
#define pli pair<ll,int>
using namespace std;
const int MAXN=1e5+9;
ll ans=0;
int n,m,q,a[100][4];
vector<int> v;
inline void recurse(int len)
{
	if(len==n)
	{
		ll res=0;
		for(int i=0;i<q;i++)
		{
			if(v[a[i][1]]-v[a[i][0]]==a[i][2])
			{
				res+=a[i][3];
			}
		}
		ans=max(ans,res);
		return;
	}
	int prev=1;
	if(!v.empty())
	{
		prev=v.back();
	}
	for(int i=prev;i<=m;i++)
	{
		v.push_back(i);
		recurse(len+1);
		v.pop_back();
	}
}
int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	cin>>n>>m>>q;
	for(int i=0;i<q;i++)
	{
		for(int j=0;j<4;j++)
		{
			cin>>a[i][j];
			if(j<2)
			{
				a[i][j]--;
			}
		}
	}
	recurse(0);
	cout<<ans<<endl;
	return 0;
}