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 java.util.*

fun main(args : Array<String>) {
    val (n, m, q) = readLine()!!.split(" ").map { it.toInt() }
    val qq = mutableListOf<Item>()

    repeat(q) {
        val (a, b, c, d) = readLine()!!.split(" ").map { it.toInt() }
        qq.add(Item(a-1, b-1, c, d))
    }

    val dfs = Stack<IntArray>()
    dfs.push(IntArray(n){0})

    var max = 0

    while (dfs.isNotEmpty()) {
        val a = dfs.pop()
        if (a.last() != 0) {
            var score = 0
            qq.forEach {
                if (a[it.idx2] - a[it.idx1] == it.diff) score += it.score
            }
            max = Math.max(max, score)
            continue
        }

        if (a[0] == 0) {
            for (i in 1..m) {
                val newA = a.copyOf()
                newA[0] = i
                dfs.push(newA)
            }
            continue
        }

        val lastIdx = a.indexOfLast { it != 0 }
        for (i in a[lastIdx]..m) {
            val newA = a.copyOf()
            newA[lastIdx+1] = i
            dfs.push(newA)
        }
    }

    println(max)
}

data class Item(val idx1: Int, val idx2: Int, val diff: Int, val score: Int)