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 std::io::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char) 
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let n: usize = read();
    let m: usize = read();
    let q: usize = read();

    let mut v: Vec<(usize, usize, usize, usize)> = Vec::new();
    let mut max: usize = 0;
    for _ in 0..q {
        let a: usize = read();
        let b: usize = read();
        let c: usize = read();
        let d: usize = read();
        v.push((a, b, c, d));
        max += d;
    }
    let mut a: Vec<usize> = vec![1; n];
    let mut sum: usize = 0;
    while a[0] <= 10 {
        let mut tmp: usize = 0;
        for (ai, bi, ci, di) in &v {
            if a[*bi-1] == a[*ai-1] + *ci {
                tmp += *di;
            }
        }
        if sum < tmp {
            sum = tmp;
        }
        let g = kuriage(&mut a, n-1, m);
        if g.is_none() || max == sum {
            break;
        }
    }
    println!("{}", sum);
}

fn kuriage(a: &mut Vec<usize>, k: usize, m: usize) -> Option<&mut Vec<usize>> {
    if a[k] < m {
        a[k] += 1;
        return Some(a);
    } else {
        if k == 0 {
            return None;
        }
        a[k] = 0;
        return kuriage(a, k-1, m);
    }
}