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-mcs 6.8.0.105) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
class abc165_d{
  public static void Main(){
    String[] str = Console.ReadLine().Split(' ');
    ulong a = ulong.Parse(str[0]);
    ulong b = ulong.Parse(str[1]);
    ulong n = ulong.Parse(str[2]);
    ulong ans = 0, min, max;
    for(ulong x = 0; x <= n; x++){
      min = x/b;
      max = a*x/b;
      ulong temp = max-min*a;
      if(ans < temp)
        ans = temp;
    }
    Console.WriteLine(ans);
  }
}