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) {
		Scanner stdIn = new Scanner(System.in);
		double A = stdIn.nextLong();
		double B = stdIn.nextLong();
		long N = stdIn.nextLong();
		
		long max = sub(A, B, 1);
		
		for(int i = 2; i <= N; i ++) {
			max = Math.max(max, sub(A, B, i));
		}
		System.out.println(max);
	}
	
	public static long sub(double A, double B, long x) {
		return (long) (Math.floor(A * x / B) - A * Math.floor(x / B));
	}

}