Problem:
Score : 400 points

Problem Statement

Given are integers A, B, and N.

Find the maximum possible value of floor(Ax/B) - A × floor(x/B) for a non-negative integer x not greater than N.

Here floor(t) denotes the greatest integer not greater than the real number t.

Constraints

1 ≤ A ≤ 10^{6}

1 ≤ B ≤ 10^{12}

1 ≤ N ≤ 10^{12}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B N

Output

Print the maximum possible value of floor(Ax/B) - A × floor(x/B) for a non-negative integer x not greater than N, as an integer.

Sample Input 1

5 7 4

Sample Output 1

2

When x=3, floor(Ax/B)-A×floor(x/B) = floor(15/7) - 5×floor(3/7) = 2. This is the maximum value possible.

Sample Input 2

11 10 9

Sample Output 2

9

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;
import java.io.*;
public class Main {
        public static void main(String[] args){
                Scanner sc = new Scanner(System.in);
                Map hs = new HashMap();
                PrintWriter ou = new PrintWriter(System.out);
                int a = Integer.parseInt(sc.next());
                long b = Long.parseLong(sc.next());
                long n = Long.parseLong(sc.next());
                sc.close();
                ou.print((int)(Math.floor(a * Math.min(b - 1 , n) * 1.0 / b) - a * Math.floor(Math.min(b - 1 , n) * 1.0 / b)) + "\n");
                ou.flush();
        }
}