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 scala.io.StdIn

object Main extends App {
  val Array(n, m, q) = StdIn.readLine().split(" ").map(_.toInt)
  val a = (0 until q).map { _ =>
    val Array(a, b, c, d) = StdIn.readLine().split(" ").map(_.toInt)
    Item(a - 1, b - 1, c, d)
  }

  var best = 0
  def f(x: Int, n: Int, list: Vector[Int]): Unit = {
    if (x <= m) {
      if (n == 0) {
        val res = a.foldLeft(0) { case (acc, Item(a, b, c, d)) =>
          if (list(b) - list(a) == c) acc + d else acc
        }
        best = best max res
      } else {
        for (i <- x to m)
          f(i, n - 1, list :+ i)
      }
    }
  }
  f(1, n, Vector.empty)
  println(best)

  case class Item(a: Int, b: Int, c: Int, d: Int)

  def readIntPair: (Int, Int) = {
    val Array(x, y) = StdIn.readLine().split(" ").map(_.toInt)
    (x, y)
  }
}