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.Text;
using System.Threading.Tasks;
using System.IO;

namespace ABC
{
    class ABC165D
    {
        const bool TESTING = false;
        const string FILE = "/tmp/data.txt";

        static void Main(string[] args)
        {
            if (TESTING)
            {
                Console.SetIn(new StreamReader(FILE));
            }
            var line = Console.ReadLine();
            var sa = line.Split(' ');
            long a = long.Parse(sa[0]);
            long b = long.Parse(sa[1]);
            long n = long.Parse(sa[2]);

            long result = 0;
            if (n < b)
            {
                result = proc(a, b, n);
            }
            else
            {
                result = proc(a, b, b - 1);
            }
            /*
            for (long x = b - 1; x <= n; x += b)
            {
                /*
                long r = proc(a, b, x);
                if (r >= result)
                {
                    result = r;
                }
                else
                {
                    break;
                }
                result = Math.Max(result, proc(a, b, x));
//                Console.WriteLine("" + x + ":" + proc(a, b, x));
            }
        */
            Console.WriteLine(result);

#if DEBUG
            Console.WriteLine();
#endif
        }

        private static long proc(long a, long b, long x)
        {
            return (a * x) / b - a * (x / b);
        }
    }
}