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;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder.Abc
{
    class QuestionD
    {
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            // 整数配列の入力
            var abn = Console.ReadLine().Split(' ').Select(q => long.Parse(q)).ToArray();

            var a = abn[0];
            var b = abn[1];
            var n = abn[2];

            var max = long.MinValue;

            long j = 0; ;

            for(long i = 0; true; i++) {
                j = ((b * i) + a - 1) / a;
                if(j > n) {
                    break;
                }

                var z = (a * j) / b;
                var s = a * (j / b);
                max = Math.Max(z - s, max);

                if (max == a - 1 || max == ((a * (b - 1)) / b)) {
                    break;
                }
            }

            Console.WriteLine(max);

            Console.Out.Flush();
        }
    }
}