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# (Mono-csc 3.5.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;

class Program
{
    public static void Main()
    {
        var n = ReadLine().Split().Select(a => long.Parse(a)).ToArray();
        if(n[0] == 1 || n[1] == 1)
        {
            WriteLine($"{0}");
            return;
        }
        if(n[2] == 1)
        {
            WriteLine($"{(long)((n[0] * 1) / (double)n[1]) - n[0] * (long)(1 / (double)n[1])}");
            return;
        }
        long count = Min(n[1] - 1, n[2]);
        long before = 0, current = 0, after = 0;
        long max = 0;
        while(0 < count)
        {
            before = (long)((n[0] * (count - 1)) / (double)n[1]) - n[0] * (long)((count - 1) / (double)n[1]);
            current = (long)((n[0] * count) / (double)n[1]) - n[0] * (long)(count / (double)n[1]);
            after = (long)((n[0] * (count + 1)) / (double)n[1]) - n[0] * (long)((count + 1) / (double)n[1]);
            max = Max(max, current);
            if(after <= current && before < current || after < current && before <= current)
            {
                WriteLine($"{current}");
                return;
            }
            count--;
        }
        WriteLine($"{max}");
    }
}