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

object Main {
  def main(args: Array[String]): Unit = {
    //nextLineとnextを同時に使ったら死ぬ
    val sc = new Scanner(System.in)

    val n, m, q = sc.nextInt()

    val ar = bfs((1 to m).map(a => Array(a)).toArray, m, n)

    val nums = Array.fill(q) {
      val a, b, c = sc.nextInt()
      val d = sc.nextLong()
      (a, b, c, d)
    }

    val ans =
      ar.map(list => {
        nums.map {
          case (a, b, c, d) =>
            if (list(b - 1) - list(a - 1) == c) d else 0
        }.sum
      })

    println(ans.max)

//    debug((1 to m).toArray.mkString(" "))
//    ar.foreach(ar => debug(ar.mkString(" ")))
//    nums.foreach(debug(_))
  }

  @scala.annotation.tailrec
  def bfs(arr: Array[Array[Int]], m: Int, n: Int): Array[Array[Int]] = {
    if (arr.head.length == n) {
      arr
    } else {
      bfs(arr.flatMap(ar => {
        for (i <- ar.last to m) yield {
          ar :+ i
        }
      }), m, n)
    }
  }

  @scala.annotation.tailrec
  def gcd(a: Int, b: Int): Int = {
    if (b == 0) a else gcd(b, a % b)
  }
  def debug(args: Any*): Unit = {
    Console.err.println(args.mkString(" "))
  }
}