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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Windows;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Atcoder
{
    public class Program
    {
        static void Main(string[] args)
        {
            var r = ReadSplit();
            var a = r[0].Double();
            var b = r[1].Double();
            var n = r[2].Double();
            var x = n;
            double max = n;
            double min = 1;
            Double ans = Math.Floor(a * x/ b) - a * Math.Floor(x / b);
            while (max - min > 1)
            {
                x = Math.Floor(min + (max - min) / 2);
                var tmp = Math.Floor(a * x/ b) - a * Math.Floor(x / b);
                var tmpUp = Math.Floor(a * (x + 1) / b) - a * Math.Floor((x + 1) / b);
                if (tmp <= tmpUp) min = x;
                else max = x;
                if (tmp > ans)
                {
                    ans = tmp;
                }
            }
            WriteRead(ans);
        }

        public class Permutation
        {
            public IEnumerable<T[]> Enumerate<T>(IEnumerable<T> items)
            {
                return _GetPermutations<T>(new List<T>(), items.ToList());
            }

            private IEnumerable<T[]> _GetPermutations<T>(IEnumerable<T> perm, IEnumerable<T> items)
            {
                if (items.Count() == 0)
                {
                    yield return perm.ToArray();
                }
                else
                {
                    foreach (var item in items)
                    {
                        var result = _GetPermutations<T>(perm.Concat(new T[] { item }),
                                                            items.Where(x => x.Equals(item) == false)
                                        );
                        foreach (var xs in result)
                            yield return xs.ToArray();
                    }
                }
            }
        }

        public static string Read()
        {
            return Console.ReadLine();
        }

        public static string[] ReadSplit()
        {
            return Console.ReadLine().Split(' ');
        }

        public static void WriteRead(object str)
        {
            Console.WriteLine(str);
            Read();
        }

        public static void Write(object str)
        {
            Console.WriteLine(str);
        }

        private static bool ChangeMin<T>(ref T a, T b) where T : IComparable
        {
            if (a.CompareTo(b) > 0)
            {
                a = b;
                return true;
            }
            return false;
        }

        private static bool ChangekMax<T>(ref T a, T b) where T : IComparable
        {
            if (b.CompareTo(a) > 0)
            {
                a = b;
                return true;
            }
            return false;
        }
    }
}


public static class Extentions
{
    public static int Int(this object obj)
    {
        return int.Parse(obj.ToString());
    }

    public static long Long(this object obj)
    {
        return long.Parse(obj.ToString());
    }

    public static decimal Decimal(this object obj)
    {
        return decimal.Parse(obj.ToString());
    }

    public static double Double(this object obj)
    {
        return double.Parse(obj.ToString());
    }

    public static T2 GetValueZero<T1, T2>(this Dictionary<T1, T2> d, T1 key) where T2 : struct
    {
        T2 value;
        if (d.TryGetValue(key, out value))
        {
            return value;
        }
        return new T2();
    }
}