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 <bits/stdc++.h>
using namespace std;

int main()
{
    int N, M, Q;
    cin >> N >> M >> Q;
    vector<int> a(Q);
    vector<int> b(Q);
    vector<int> c(Q);
    vector<int> d(Q);
    for (int i = 0; i < Q; i++)
    {
        cin >> a.at(i) >> b.at(i) >> c.at(i) >> d.at(i);
    }
    int ans = 0;
    int hozonnum = 0;
    if (Q == 1)
    {
        cout << d.at(0);
        exit(0);
    }
    

    vector<int> hozon(N);

    for (int i = 1; i <= M; i++)
    {
        hozon.at(0) = i; 
        for (int j = i; j <= M; j++)
        {
            hozon.at(1) = j;
            for (int k = j; k <= M; k++)
            {
                if (N == 2)
                {
                    for (int g = 0; g < Q; g++)
                    {
                        if (hozon.at(b.at(g)-1) == hozon.at(a.at(g)-1) + c.at(g))
                        {
                            ans += d.at(g);
                        }
                    }
                    if (hozonnum < ans)
                    {
                        hozonnum = ans;
                    }
                    ans = 0;
                    break;
                }
                hozon.at(2) = k;
                
                for (int x = k; x <= M; x++)
                {
                    if (N == 3)
                    {
                        for (int g = 0; g < Q; g++)
                        {
                            if (hozon.at(b.at(g)-1) == hozon.at(a.at(g)-1) + c.at(g))
                            {
                                ans += d.at(g);
                            }
                        }
                        if (hozonnum < ans)
                        {
                            hozonnum = ans;
                        }
                        ans = 0;
                        break;
                    }
                    hozon.at(3) = x;
                    
                    for (int y = x; y <= M; y++)
                    {
                        if (N == 4)
                        {
                            for (int g = 0; g < Q; g++)
                            {
                                if (hozon.at(b.at(g)-1) == hozon.at(a.at(g)-1) + c.at(g))
                                {
                                    ans += d.at(g);
                                }
                            }
                            if (hozonnum < ans)
                            {
                                hozonnum = ans;
                            }
                            ans = 0;
                            break;
                        }
                        hozon.at(4) = y;
                        
                        for (int z = y; z <= M; z++)
                        {
                            if (N == 5)
                            {
                                for (int g = 0; g < Q; g++)
                                {
                                    if (hozon.at(b.at(g)-1) == hozon.at(a.at(g)-1) + c.at(g))
                                    {
                                        ans += d.at(g);
                                    }
                                }
                                if (hozonnum < ans)
                                {
                                    hozonnum = ans;
                                }
                                ans = 0;
                                break;
                            }
                            hozon.at(5) = z;
                            
                            for (int q = z; q <= M; q++)
                            {
                                if (N == 6)
                                {
                                    for (int g = 0; g < Q; g++)
                                    {
                                        if (hozon.at(b.at(g)-1) == hozon.at(a.at(g)-1) + c.at(g))
                                        {
                                            ans += d.at(g);
                                        }
                                    }
                                    if (hozonnum < ans)
                                    {
                                        hozonnum = ans;
                                    }
                                    ans = 0;
                                    break;
                                }
                                hozon.at(6) = q;
                                
                                for (int p = q; p <= M; p++)
                                {
                                    if (N == 7)
                                    {
                                        for (int g = 0; g < Q; g++)
                                        {
                                            if (hozon.at(b.at(g)-1) == hozon.at(a.at(g)-1) + c.at(g))
                                            {
                                                ans += d.at(g);
                                            }
                                        }
                                        if (hozonnum < ans)
                                        {
                                            hozonnum = ans;
                                        }
                                        ans = 0;
                                        break;
                                    }
                                    hozon.at(7) = p;
                                    for (int w = p; w <= M; w++)
                                    {
                                        if (N == 8)
                                        {
                                            for (int g = 0; g < Q; g++)
                                            {
                                                if (hozon.at(b.at(g)-1) == hozon.at(a.at(g)-1) + c.at(g))
                                                {
                                                    ans += d.at(g);
                                                }
                                            }
                                            if (hozonnum < ans)
                                            {
                                                hozonnum = ans;
                                            }
                                            ans = 0;
                                            break;
                                        }
                                        hozon.at(8) = w;
                                        for (int l = w; l <= M; l++)
                                        {
                                            if (N == 9)
                                            {
                                                for (int g = 0; g < Q; g++)
                                                {
                                                    if (hozon.at(b.at(g)-1) == hozon.at(a.at(g)-1) + c.at(g))
                                                    {
                                                        ans += d.at(g);
                                                    }
                                                }
                                                if (hozonnum < ans)
                                                {
                                                    hozonnum = ans;
                                                }
                                                ans = 0;
                                                break;
                                            }

                                            hozon.at(9) = l;
                                            if (N == 10)
                                            {
                                                for (int g = 0; i < Q; g++)
                                                {
                                                    if (hozon.at(b.at(g)-1) == hozon.at(a.at(g)-1) + c.at(g))
                                                    {
                                                        ans += d.at(g);
                                                    }
                                                    
                                                }
                                                if (hozonnum < ans)
                                                {
                                                    hozonnum = ans;
                                                }
                                                ans = 0;
                                                
                                            }
                                            
                                            
                                        }
                                        
                                    }
                                    
                                    
                                }
                                
                            }
                            
                        }
                        
                    }
                    
                }
                
            }
            
        }
        
    }
    
    cout << hozonnum;
    
}