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.util.*;

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 n_div_max = n/b;

        long base = 1;
        long res = 0;
        while(base<=2){
            long x = b*base - 1;
            if(x>n)x=n;
            long floor_xB = base-1;
            long floor_AxB = (a*x)/b;
            res = Math.max(res, floor_AxB-a*floor_xB);
            base++;
        }

        System.out.println(res);

    }
}