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: Accepted)

package main

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

func main() {
	sc := NewScanner()

	n := sc.ReadInt()
	m := sc.ReadInt()
	q := sc.ReadInt()
	abcds := make([]ABCD, q)
	for i := 0; i < q; i++ {
		a := sc.ReadInt()
		b := sc.ReadInt()
		c := sc.ReadInt()
		d := sc.ReadInt()
		abcds[i] = ABCD{a, b, c, d}
	}

	cur := make(SeqA, n)
	for i := 0; i < n-1; i++ {
		// the last is 0
		cur[i] = 1
	}

	maxScore := 0
	for {
		var ok bool
		ok, cur = nextSeqA(n, m, cur)
		if !ok {
			break
		}

		score := computeScore(abcds, cur)
		if score > maxScore {
			maxScore = score
		}
	}

	fmt.Println(maxScore)
}

func nextSeqA(n int, m int, cur SeqA) (bool, SeqA) {
	carryDigitCount := 0
	for i := n - 1; i >= 0; i-- {
		if cur[i] == m {
			carryDigitCount++
		} else {
			break
		}
	}

	if carryDigitCount == 0 {
		cur[n-1]++
		return true, cur
	} else if carryDigitCount == n {
		return false, nil
	} else {
		min := cur[n-1-carryDigitCount] + 1
		for i := 0; i <= carryDigitCount; i++ {
			cur[n-1-i] = min
		}
		return true, cur
	}
}

func computeScore(abcds []ABCD, seqA SeqA) int {
	totalD := 0
	for _, abcd := range abcds {
		if seqA[abcd.B-1]-seqA[abcd.A-1] == abcd.C {
			totalD += abcd.D
		}
	}
	return totalD
}

type SeqA []int

type ABCD struct {
	A int
	B int
	C int
	D int
}

// util
// *   math/simple

func Abs(x int) int {
	if x >= 0 {
		return x
	}
	return -x
}

func Min(values ...int) int {
	if len(values) == 0 {
		panic("no values")
	}
	min := values[0]
	for _, v := range values {
		if v < min {
			min = v
		}
	}
	return min
}

func Max(values ...int) int {
	if len(values) == 0 {
		panic("no values")
	}
	max := values[0]
	for _, v := range values {
		if v > max {
			max = v
		}
	}
	return max
}

func Pow(base int, exponent uint) int {
	answer := 1
	for i := uint(0); i < exponent; i++ {
		answer *= base
	}
	return answer
}

// *   io

type Scanner struct {
	bufScanner *bufio.Scanner
}

func NewScanner() *Scanner {
	bufSc := bufio.NewScanner(os.Stdin)
	bufSc.Split(bufio.ScanWords)
	bufSc.Buffer(nil, 100000000)
	return &Scanner{bufSc}
}

func (sc *Scanner) ReadString() string {
	bufSc := sc.bufScanner
	bufSc.Scan()
	return bufSc.Text()
}

func (sc *Scanner) ReadInt() int {
	bufSc := sc.bufScanner
	bufSc.Scan()
	text := bufSc.Text()

	num, err := strconv.Atoi(text)
	if err != nil {
		panic(err)
	}
	return num
}