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 _165_d
{
    internal class FloorFunction
    {
        private static void Main(string[] args)
        {
            var abn = Console.ReadLine()?.Split(' ').Select(decimal.Parse).ToArray();
            if (abn == null) return;
            var a = abn[0];
            var b = abn[1];
            var n = abn[2];


            var list = new List<decimal>();
            for (decimal x = 0; x <= n; x++)
            {
                list.Add(Math.Floor(a * x / b) - a * Math.Floor(x / b));
            }

            list.Sort();
            list.Reverse();
            Console.WriteLine(list[0]);
        }
    }
}