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)

fun main(args: Array<String>) = ABC165C.main()

object ABC165C {
    fun log(message: Any?) {
        println(message)// TODO: ←消す
    }

    fun main() {
        val (N, M, Q) = readInts()
        val tuples = (1..Q).map { readInts() }  // a,b,c,d

        val arrays = (1..M).combination(N)
            //.onEach { log(it) }
            .toList()

        val scores = arrays.map { it.calcScore(tuples) }
        val ans = scores.max()

        println(ans)
    }

    fun List<Int>.calcScore(tuples: List<List<Int>>): Long {
        return tuples.map { (a, b, c, d) ->
            if (this[b-1]-this[a-1] == c) d.toLong() else 0L
        }.sum()
    }

    /*####################################################################################*/

    fun readString() = readLine()!!
    fun readStrings() = readLine()!!.split(" ")
    fun readInt() = readLine()!!.toInt()
    fun readInts() = readLine()!!.split(" ").map { it.toInt() }


    class Combination<T> : BasicCombinator<T>() {
        override fun List<T>.chooseRemains(i: Int): List<T> = this.drop(i)
    }

    fun IntRange.combination(k: Int): Sequence<List<Int>> = this.toList().combination(k)
    fun <T> List<T>.combination(k: Int): Sequence<List<T>> = Combination<T>().generate(this, k)

    abstract class BasicCombinator<T> {
        abstract fun List<T>.chooseRemains(i: Int): List<T>

        fun generate(items: List<T>, k: Int): Sequence<List<T>> {
            when {
                (k < 0) ->
                    throw IllegalArgumentException()
                (k == 0) ->
                    return emptySequence()
                (k == 1) ->
                    return items.asSequence().map { listOf(it) }
                else ->
                    return items.asSequence().mapIndexed { index, first ->
                        val remains = items.chooseRemains(index)
                        generate(remains, k - 1).map { first + it }
                    }.flatten()
            }
        }

        private operator fun T.plus(other: List<T>): List<T> {
            val list = mutableListOf(this)
            list.addAll(other)
            return list
        }
    }
}