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: Wrong Answer)

import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		var sc = new Scanner(System.in);
		var a = sc.nextLong();
		var b = sc.nextLong();
		var n = sc.nextLong();
		sc.close();

		var max = 0L;
		if (b <= 1000000 || n <= 1000000) {
			for (var i = Math.max(0, n - 1000000); i <= n; i++) {
				var result = (long) Math.floor(a * i / b) - a * (long) Math.floor(i / b);
				max = Math.max(max, result);
			}
		} else {
			for (var i = Math.min(b - 1, n); i <= n; i += b) {
				var result = (long) Math.floor(a * i / b) - a * (long) Math.floor(i / b);
				max = Math.max(max, result);
			}
		}
		System.out.println(max);
	}
}