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;
using System.Collections.Generic;
using System.ComponentModel;
using System.ComponentModel.Design;
using System.IO.Compression;
using System.Linq;
using System.Numerics;
using System.Text;

namespace Atcoder
{
    class Program
    {
        private const long COMDIV = 1000000007;
        static void Main(string[] args)
        {
            var ABN = Console.ReadLine().Split().Select(decimal.Parse).ToArray();
            decimal ret = -1;
            for (long x = 0; x <= ABN[2]; x++)
            {
                var tmp = Math.Floor(ABN[0] * x / ABN[1]) - ABN[0] * Math.Floor(x / ABN[1]);
                ret = Math.Max(ret, tmp);
            }

            Console.WriteLine(ret);
            //Math.Floor()
        }
        
    }
}