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.Collections.Generic;
using System.Linq;

namespace AtCoderApp
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = Console.ReadLine().Split(' ');
            var A = ulong.Parse(input[0]);
            var B = ulong.Parse(input[1]);
            var N = ulong.Parse(input[2]);

            double maxValue = 0;

            for (ulong i = 1; i <= N; i++)
            {
                var sahen = Math.Floor(A * i / (double)B);
                var uhen = A * Math.Floor(i / (double)B);

                var fx = sahen - uhen;
                if (fx >= maxValue)
                {
                    maxValue = fx;
                }
                else
                {
                    break;
                }
            }
            Console.WriteLine(maxValue);
        }
    }
}