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: Wrong Answer)

#include<stdio.h>
int main(void){
 long long int a,b,c,d,e,f,g,m,x,y;
long long int A[1000][4];
int long long B[15]={1,1,1,1,1,1,1,1,1,1,1,1,1,1,1};
f=1;
x=0;
y=0;

scanf("%lld",&a);
scanf("%lld",&b);
scanf("%lld",&c);
for(d=0;d<c;d++)
{ 
    for(g=0;g<4;g++){
        scanf("%lld",&A[d][g]);
        
    }
}
for(d=0;d<a;d++){
       

    f=f*b;
    
}

for(d=0;d<f;d++){
           

    
    m=1;
    for(g=a;g>0;g--){      

    if(B[g]==b){
B[g]=1;
    }else
    if(m==0){
}else{
    B[g]=B[g]+1;
    m=0;
}
    }
    for(g=0;g<c;g++){       

        if(B[A[g][1]]-B[A[g][0]]==A[g][2]){
x=x+A[g][3];
        }
    }

    if(x>y){
        y=x;
    }
    x=0;
    }
    printf("%lld",y);
    
    
}