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.Scanner;

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

}