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;

class Program
{
    static void Main () 
    {
        String[] inline = Console.ReadLine().Split(' ');
        ulong a = ulong.Parse(inline[0]);
        ulong b = ulong.Parse(inline[1]);
        ulong n = ulong.Parse(inline[2]);
        ulong ans = 0;
        if (b > n)
        {
            ;
            ans = (ulong) Math.Floor( (decimal) (a*n / b));
        }
        else if (b == n)
        {
            ans = (ulong) Math.Floor((decimal) (a*(n-1) / b));
        }
        else
        {
            ulong s = (ulong) Math.Floor((decimal) (a*(b-1) / b));
            ans = s;
            for (ulong i = b; i <= n; i++)
            {
                ulong t = (ulong) (Math.Floor((decimal) (a*i / b)) - a * Math.Floor((decimal) (i / b)));
                ans = Math.Max(ans,t);
            }
        }
        Console.WriteLine(ans);
    }
}