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) throws Exception {
        
        Scanner sc = new Scanner(System.in);

        long a = sc.nextLong();
        long b = sc.nextLong();
        long n = sc.nextLong();

        long l = 1;
        long r = n;
        long max = 0;
        while(l <= r){
            long center = (l + r)/2;
            long temp = a*center/b - center/b*a;
            if(max < temp){
                max = temp;
            }
            if(temp < 0){
                r = center-1;
            }else {
                break;
            }
        }
        for(long i=l; i<=r; i++){
            long temp = a*i/b - i/b*a;
            if(max<temp){
                max=temp;
            }
        }
        System.out.println(max);
    }
}