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 <stdio.h>
#include <stdlib.h>
#define MAX(x,y) ((x)<(y)?(y):(x))

typedef long long ll;

typedef struct Hoge{
    int a;
    int b;
    int c;
    int d;
}hoge;

void search(int i,int N,int M,int Q,int *A,hoge *AL,ll *max){
    if(i==M+1){
        int tmp = 0;
        for(int q = 0;q<Q;q++){
            if(A[AL[q].b]- A[AL[q].a] == AL[q].c) tmp+=AL[q].d;
        }
        *max = MAX(*max,tmp);
    }else if(i==1){
        for(int j = 1;j<=M;j++){
            A[i]=j;
            search(i+1,N,M,Q,A,AL,max);
        }
    }else{
        for(int j = A[i-1];j<=M;j++){
            A[i]=j;
            search(i+1,N,M,Q,A,AL,max);
        }
    }
}

int main(){
    int N,M,Q;
    scanf("%d %d %d",&N,&M,&Q);
    int A[N];
    hoge AL[Q];
    for(int i = 0;i<N;i++) A[i]=0;
    ll ans=0;
    for(int i = 0;i<Q;i++)scanf("%d %d %d %d",&AL[i].a,&AL[i].b,&AL[i].c,&AL[i].d);
    search(1,N,M,Q,A,AL,&ans);
    printf("%lld\n",ans);
    
    return 0;
}