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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using System.Text.RegularExpressions;

class Program
{
    static int[] ReadInts()
        => Console.ReadLine()
            .Split(new[] { ' ', '\t' }, StringSplitOptions.RemoveEmptyEntries)
            .Select(s => int.Parse(s))
            .ToArray();

    static void Main(string[] args)
    {
        var numbers = Console.ReadLine()
            .Split(new[] { ' ', '\t' }, StringSplitOptions.RemoveEmptyEntries)
            .Select(s => BigInteger.Parse(s))
            .ToArray();
        var a = numbers[0];
        var b = numbers[1];
        var n = numbers[2];
        var x = BigInteger.Min(b - 1, n);
        var result = a * x / b;
        Console.WriteLine(result.ToString());
    }
}