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 Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var abn = Console.ReadLine().Split().Select(s => long.Parse(s)).ToArray();
            long a = abn[0];
            long b = abn[1];
            long n = abn[2];
            long max = 0;
            for (int i = 1; i <= n ; i++)
            {
                if (i >= b) break;

                long temp = Convert.ToInt64(Math.Floor((double)a * i / b)
                    - a * Math.Floor((double)i / b));

                if (temp >= max) max = temp;

            }

            Console.WriteLine(max);
        }
    }
}