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: Time Limit Exceeded)

import java.util.*;
import java.math.*;
     
class Main{
    public static void main(String[] args) {
        
        try(Scanner sc = new Scanner(System.in)){

            double a = sc.nextLong();
            double b = sc.nextLong();
            double n = sc.nextLong();

            double ans = 0;
            double maxD = 0;
            for(double x = 1; x <= n; x++){
                double d = x%b;
                if(maxD < d){
                    ans = Math.floor(a*x/b) - a*Math.floor(x/b);
                }
            }

            System.out.println((long)ans);

        }catch(Exception e){
            e.printStackTrace();
        }        
    }
}