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.Scanner;

public class Main {

    public static void main(String[] args) {
        var scaner = new Scanner(System.in);
        var a_b_n = scaner.nextLine().split(" ");
        var a = Long.parseLong(a_b_n[0]);
        var b = Long.parseLong(a_b_n[1]);
        var n = Long.parseLong(a_b_n[2]);
        scaner.close();

        var x = 0;
        long r = 0;
        for(;x <= n; x++) {
            var tmp = (a*x / b) - a*(x / b);
            if(r<tmp) {
                r = (long)tmp;
            }
        }
        System.out.println(r);
    }

}