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.math.BigInteger;
import java.util.Scanner;

class Main {
    public static void main(final String[] args) {
        Scanner sc = new Scanner(System.in);
        BigInteger a = new BigInteger(sc.next());
        BigInteger b = new BigInteger(sc.next());
        BigInteger n = new BigInteger(sc.next());

        BigInteger max = BigInteger.ZERO;

        for (BigInteger i = BigInteger.ONE; i.compareTo(n) <= 0; i = i.add(BigInteger.ONE)) {
            BigInteger tmp = (a.multiply(i).divide(b)).subtract(a.multiply(i.divide(b)));
            if (tmp.compareTo(max) >= 0) {
                max = tmp;
            }
        }

        System.out.println(max);    

    }
}