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 {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long A = sc.nextLong();
        long B = sc.nextLong();
        long N = sc.nextLong();
        sc.close();

        if (A * N < B) {
            System.out.println(0);
            return;
        }

        long max = -1;
        for (long x = N; x >= 0; x--) {
            if (x < B - 1 && max != -1) {
                break;
            }
            long letMax = (long) (A * x / B) - A * (long) (x / B);
            if (letMax >= max) {
                max = letMax;
            }
        }

        System.out.println(max);
    }
}