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 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.math.*;
import java.util.*;
public class Main{

	public static void main(String[] args) {
		long mod = (long)(1e9+7);
		Scanner input = new Scanner(System.in);
		long A = input.nextLong();
		long B = input.nextLong();
		long N = input.nextLong();
		if (B==1) System.out.println(0);
		else {
			long max = A*N/B-N/B*A;
			for (long x = B-1; x <= N; x+=B) {
				long factor = x/B;
				long cur = A*x/B-factor*A;
				max = Math.max(max, cur);
			}
			System.out.println(max);
		}
	}
}