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;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace D
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var abn = Console.ReadLine().Trim().Split(' ').Select(double.Parse).ToArray();
            Func<long, long> f = x => (long)(Math.Floor((abn[0] * x) / (double)abn[1]) - abn[0] * Math.Floor(x / (double)abn[1]));
            var max = 0L;
            var index = (abn[1] < abn[2]) ? (long)(abn[1] - 1) : (long)abn[2];
            while (index <= abn[1] && index >= 0)
            {
                var tmp = f(index--);
                if (tmp >= max) max = tmp;
                else break;
            }
            Console.WriteLine(max);
        }
    }
}