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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        D solver = new D();
        solver.solve(1, in, out);
        out.close();
    }

    static class D {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            // 入力
            long a = Long.parseLong(in.next());
            long b = Long.parseLong(in.next());
            long n = Long.parseLong(in.next());
            long ans = -1;
            long cnt = b;

            if (n < b) cnt = n;
            for (int i = 1; i <= cnt; i++) {
                long tmp = f(a, b, i);
                if (tmp - ans < 0) {
                    break;
                }
                ans = Math.max(ans, tmp);
            }

            // 出力
            out.println(ans);

        }

        public static long f(long a, long b, long x) {
            long res = 0;
            res = (long) (Math.floor(a * x / b) - a * Math.floor(x / b));
            return res;
        }

    }
}