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;

class D
{
    static void Main()
    {
#if DEBUG
        string exampleInput =
        @"50000 700000 40000000000
";
        Console.SetIn(new System.IO.StringReader(exampleInput));
#endif

        var ABN = Console.ReadLine().Split(' ').Select(long.Parse).ToList();
        var A = ABN[0];
        var B = ABN[1];
        var N = ABN[2];
        var rmax = A * N / B - A * (N / B);
        if(N >= B)
        {
            var kmax = (N + 1) / B;
            
            for (long k = kmax; k >= Math.Max(1, kmax - 10000); k--)
            {
                var x = k * B - 1;
                var r = A * x / B - A * (x / B);
                rmax = Math.Max(rmax, r);
            }
        }
        Console.WriteLine(rmax);
        Console.Out.Flush();
    }
}