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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main {
	public static void main(String[] args) {
		FastScanner sc = new FastScanner(System.in);
		long a = sc.nextLong(), b = sc.nextLong(), n = sc.nextLong();
		
		long x = Math.min(n, b-1);
		System.out.println(a*x/b-a*(x/b));
	}
	
	static class FastScanner {
			private BufferedReader reader = null;
		    private StringTokenizer tokenizer = null;
		    public FastScanner(InputStream in) {
		        reader = new BufferedReader(new InputStreamReader(in));
		        tokenizer = null;
		    }

		    public String next() {
		        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
		            try {
		                tokenizer = new StringTokenizer(reader.readLine());
		            } catch (IOException e) {
		                throw new RuntimeException(e);
		            }
		        }
		        return tokenizer.nextToken();
		    }

		    public String nextLine() {
		        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
		            try {
		                return reader.readLine();
		            } catch (IOException e) {
		                throw new RuntimeException(e);
		            }
		        }

		        return tokenizer.nextToken("\n");
		    }

		    public long nextLong() {
		        return Long.parseLong(next());
		    }

		    public int nextInt() {
		        return Integer.parseInt(next());
		    }

		    public double nextDouble() {
		         return Double.parseDouble(next());
		     }

		    public int[] nextIntArray(int n) {
		        int[] a = new int[n];
		        for (int i = 0; i < n; i++)
		            a[i] = nextInt();
		        return a;
		    }

		    public long[] nextLongArray(int n) {
		        long[] a = new long[n];
		        for (int i = 0; i < n; i++)
		            a[i] = nextLong();
		        return a;
		    }
		}
}