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.*;
public class Main  {
   public static void main(String[] args)  {
      Scanner sc = new Scanner(System.in);
      
      long a = sc.nextLong();
      long b = sc.nextLong();
      long n = sc.nextLong();
      
      long max = 0;
      long y = 0;
      for (long i = n; i >= 0; i=i-1) {
         y = (long)Math.floor(a*i)/b - a*(long)Math.floor(i/b);
         
         if (max < y) {
            max = y;
         }   
      }
      
      System.out.println(max);
   }
}