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>) {
    val nmq = readLine()!!.split(" ")
    val n = nmq[0].toInt()
    val m = nmq[1].toInt()
    val q = nmq[2].toInt()
    val values = IntRange(1, q).map {
        val input = readLine()!!.split(" ")
        IntNums(input[0].toInt(), input[1].toInt(), input[2].toInt(), input[3].toInt())
    }

    var permutation = mutableListOf<MutableList<Int>>()
    for(i in 1..m) {
        createPermutation(mutableListOf(i), n, m, permutation)
    }
    val maxVal =  permutation.map { perm -> values.filter{ perm[it.b-1] - perm[it.a-1] == it.c }.map { it.d }.sum() }.max()
    print(maxVal)

}

data class IntNums(val a: Int, val b: Int, val c:Int, val d: Int)

fun createPermutation(base: MutableList<Int>, n: Int, m: Int, result: MutableList<MutableList<Int>>) {
    if(base.size == n) {
        result.add(MutableList(base.size) { i -> base[i] })
    }
    if(base.size >= n) return

    for(i in base[base.size -1]..m) {
        var newArray = MutableList(base.size) { i -> base[i] }
        newArray.add(i)
        createPermutation(newArray,n,m, result)
    }
    return
}