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: Accepted)

import kotlin.math.max

fun main(){
    val (n, m, q) = readLine()!!.split(" ").map{ it.toInt() }
    val list = mutableListOf<Data>()
    for(i in 0 until q){
        val tmp = readLine()!!.split(" ").map{ it.toInt() }

        list.add(Data(tmp[0] - 1, tmp[1] - 1, tmp[2], tmp[3]))
    }

    val seq = mutableListOf<Int>()
    println(search(seq, list, m, n))
}

fun search(seq: List<Int>, data: List<Data>, maxNumber: Int, maxLength: Int): Int {
    if(seq.size == maxLength){
        var ans = 0
        data.forEach { if(seq[it.b] - seq[it.a] == it.c) ans += it.d }
        return ans
    }else{
        var ans = 0
        val k = if(seq.isEmpty()) 1 else seq.last()
        for(i in k until maxNumber + 1){
            ans = max(ans, search(seq.toMutableList().apply { add(i) }, data, maxNumber, maxLength))
        }
        return ans
    }
}

data class Data(
    val a: Int,
    val b: Int,
    val c: Int,
    val d: Int
)