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 Kotlin (1.3.71) (judge verdict: Runtime Error)

fun main(args: Array<String>) {
    val (n,m,q) = readLine()!!.split(" ").map(String::toInt)
    var result = 0

    val value = Array(q){
        readLine()!!.split(" ").map{it.toInt()}
    }

    var list = Array(n){1}

    loop@ while(true){

        var sum = 0
        value.forEach {
            if(list[it[1] - 1] - list[it[0] - 1] == it[2]){
                sum += it[3]
            }
        }        
        if(sum > result){
            result = sum
        }

        for(i in list.indices){
            if(i == list.size - 1 && list[list.size-1] < m){
                list[list.size-1] += 1
                continue@loop
            }else if(list[i + 1] == m){
                for (k in i+1 until list.size){
                    list[k] = 2
                }
                list[i] += 1
                continue@loop
            }else if(list[0] == m){
                break@loop
            }
        }
    }

    println("${result}")
}