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 Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

func main() {
	N := nextInt()
	M := nextInt()
	Q := nextInt()

	a := make([]int, Q)
	b := make([]int, Q)
	c := make([]int, Q)
	d := make([]int, Q)

	for i := 0; i < Q; i++ {
		a[i] = nextInt() - 1
		b[i] = nextInt() - 1
		c[i] = nextInt()
		d[i] = nextInt()
	}
	candidates := make([][]int, 0)
	queue := make([]q, 0)
	queue = append(queue, q{0, []int{}})

	for len(queue) > 0 {
		item := queue[0]
		queue = queue[1:]

		if item.n > M {
			continue
		}
		if len(item.arr) == N {
			candidates = append(candidates, item.arr)
			continue
		}

		q1 := q{item.n + 1, copy(item.arr)}
		q1.arr = append(q1.arr, item.n+1)
		queue = append(queue, q1)

		q2 := q{item.n + 1, copy(item.arr)}
		queue = append(queue, q2)
	}

	ans := 0

	for j := 0; j < len(candidates); j++ {
		A := candidates[j]
		s := 0
		for i := 0; i < Q; i++ {
			if A[b[i]]-A[a[i]] == c[i] {
				s += d[i]
			}
		}
		ans = max(ans, s)
	}

	fmt.Println(ans)
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

type q struct {
	n   int
	arr []int
}

func copy(f []int) []int {
	t := make([]int, len(f))

	for i := 0; i < len(f); i++ {
		t[i] = f[i]
	}

	return t
}

func printarr(arr []int) {
	for i := 0; i < len(arr); i++ {
		print(arr[i], ",")
	}
	println()
}

var stdin = initStdin()

func initStdin() *bufio.Scanner {
	bufsize := 1 * 1024 * 1024 // 1 MB
	var stdin = bufio.NewScanner(os.Stdin)
	stdin.Buffer(make([]byte, bufsize), bufsize)
	stdin.Split(bufio.ScanWords)
	return stdin
}

func nextString() string {
	stdin.Scan()
	return stdin.Text()
}

func nextBytes() []byte {
	stdin.Scan()
	return stdin.Bytes()
}

func nextInt() int {
	i, _ := strconv.Atoi(nextString())
	return i
}

func nextInt64() int64 {
	i, _ := strconv.ParseInt(nextString(), 10, 64)
	return i
}