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 Rust (1.42.0) (judge verdict: Wrong Answer)

use proconio::input;

fn main() {
    input! {
        n: usize,
        m: usize,
        q: usize,
        abcd: [(usize, usize, usize, usize); q],
    }
    println!(
        "{}",
        multi_combinations(&(0..=m).collect(), n)
            .iter()
            .map(|able| {
                abcd.iter().fold(0, |sum, &(a, b, c, d)| {
                    sum + if able[b - 1] - able[a - 1] == c { d } else { 0 }
                })
            })
            .max()
            .unwrap()
    );
}

fn multi_combinations(a: &Vec<usize>, n: usize) -> Vec<Vec<usize>> {
    let (mut current, mut pointers, mut result) = (0, vec![0; n + 1], Vec::<Vec<usize>>::new());
    while current < n {
        for i in 0..=current {
            pointers[i] = pointers[current];
        }
        for _p in pointers[0]..a.len() {
            result.push(pointers.iter().rev().skip(1).map(|&p| a[p]).collect());
            pointers[0] += 1;
        }

        if pointers[current] >= a.len() {
            current += 1;
        }
        pointers[current] += 1;
    }
    result
}