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 static java.lang.Integer.*;
import static java.lang.Long.*;
import static java.lang.System.*;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {

    static void solve() throws Exception {
        long A = scanLong(), B = scanLong(), N = scanLong();
        long ans = -1;
        for (long i = 1; i <= N; i++) {
            long t = (long)(A * i / B) - (long)(A * (long)(i / B));
            if (ans < t) {
                ans = t;
            }
        }
        out.print(ans);
    }

    static int scanInt() throws IOException {
        return parseInt(scanString());
    }

    static long scanLong() throws IOException {
        return parseLong(scanString());
    }

    static String scanString() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;

    public static void main(String[] args) {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            solve();
            in.close();
            out.close();
        }
        catch (Throwable e) {
            e.printStackTrace();
            exit(1);
        }
    }
}