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 Scala (2.13.1) (judge verdict: Accepted)

import java.util.Scanner

import scala.annotation.tailrec
import scala.io.StdIn._

object Main extends App {

  val Array(n,m,q) = readLine().split(" ").map(_.toInt)
  val Qs = Array.fill(q) {
    val Array(a,b,c,d) = readLine().split(" ").map(_.toInt)
    Item(a-1,b-1,c,d)
  }
  case class Item(a: Int, b: Int, c: Int, d: Int)

  var ans = 0
  def solve() = {
    dfs(Vector.empty, 1, n)
    ans
  }

  def dfs(A: Vector[Int], lastNum: Int, n: Int): Unit = {
    if(lastNum <= m) {
      if(n == 0) {
        val score = Qs.foldLeft(0) { case (acc, Item(a,b,c,d)) =>
          if(A(b) - A(a) == c) acc + d else acc
        }
        ans = Math.max(score, ans)
      } else {
        for (i <- lastNum to m)
          dfs(A :+ i, i, n-1)
      }
    }
  }

  println(solve())

}