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: Runtime Error)

import java.util.Scanner

object Main extends App {
  val sc = new Scanner(System.in)
  val (n, m, q) = (sc.nextInt(), sc.nextInt(), sc.nextInt())
  val records = (1 to q).map { _ =>
    val (a, b, c, d) = (sc.nextInt(), sc.nextInt(), sc.nextInt(), sc.nextInt())
    Record(a, b, c, d)
  }

  val result = new MainIterator(n, m).map { ax =>
    records.map(_.point(ax)).sum
  }.max
  println(result)
}

class MainIterator(n: Int, m: Int) extends Iterator[Array[Int]] {
  private val ax = Array.fill(n)(1)
  private val end = Array.fill(n)(m)
  override def hasNext: Boolean = !ax.sameElements(end)

  override def next(): Array[Int] = {
    val upPos = if(ax.last != m) {
      Some(ax.length - 1)
    } else {
      ax.indices.reverse.tail.find { pos => ax(pos) < ax(pos + 1) }
    }
    upPos.foreach { pos =>
      ax(pos) += 1
      ((pos + 1) until ax.length).foreach(ax(_) = ax(pos))
    }
    if(upPos.isEmpty) throw new NoSuchElementException
    ax
  }
}

case class Record(a: Int, b: Int, c: Int, d: Int) {
  def point(ax: Array[Int]): Int = {
    if(ax(b - 1) - ax(a - 1) == c) d else 0
  }
}