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.io.PrintWriter
import kotlin.math.max

fun main() {
    PrintWriter(System.out).use { out ->
        solve(out)
        out.flush()
    }
}

var gn = 0
var gm = 0
var gq = 0
var max = 0
var queries = emptyArray<List<Int>>()

fun solve(out: PrintWriter) {
    val (n, m, q) = readIntegerList()
    gn = n
    gm = m
    gq = q
    queries = Array(q) { readIntegerList() }
    dfs(emptyList<Int>(), 0)
    println(max)
}

fun dfs(list: List<Int>, count: Int): Int {
    if (count == gn) {
        return calc(list)
    }

    val from = if (list.isEmpty()) 1 else list.last()
    for (i in from..gm) {
        max = max(max, dfs(list + i, count + 1))
    }
    return max
}

fun calc(list: List<Int>): Int {
    var tmp = 0
    for (q in queries) {
        val (a, b, c, d) = q
        if (list[b - 1] - list[a - 1] == c) {
            tmp += d
        }
    }
    return tmp
}

fun readInteger() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readStringList() = readLine()!!.split(" ")
fun readIntegerList() = readStringList().map(String::toInt)
fun readLongList() = readStringList().map(String::toLong)
fun readDoubleList() = readStringList().map(String::toDouble)