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: Time Limit Exceeded)

using System;
using System.ComponentModel;
using System.Linq;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            var abn = Console.ReadLine().Split(" ");
            decimal a = int.Parse(abn[0]);
            decimal b = long.Parse(abn[1]);
            decimal n = long.Parse(abn[2]);
            decimal max_v = 0;
            for (long i = 1; i <= n; i++)
            {
                decimal v = (Math.Floor(a * i / b) - a * Math.Floor(i / b));
                if (max_v < v)
                {
                    max_v = v;
                }
            }
            Console.WriteLine(max_v);
        }
    }
}