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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Diagnostics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using System.Numerics;
using System.IO;
using System.Runtime.InteropServices;
using static System.Math;
using static Math2;
using static io;
using static Utils;

public class CompetitiveProgramming
{
  public void Solve()
  {
    var (A, B, N) = Cin<long, long, long>();


    long ma = -INF;
    for (long i = N; i >= Max(0, N - 100000); --i)
    {
      ma = Max(ma, (A * i) / B - (i / B) * A);
    }
    for (int i = 0; i <= Min(N, 100000); ++i)
    {

      ma = Max(ma, (A * i) / B - A * (i / B));
    }
    Write(ma);
  }
}



public static class Math2
{
  public const int INF = 1 << 29;
  public const long INFL = 1L << 60;
  public const long MOD = 1000000007;
  public const int MOD2 = 998244353;

  public static long Power(long a, long b, long MOD = 1000000007)//i^N
  {
    long res = 1;
    while (b > 0)
    {
      if ((b & 1) != 0) res = res * a % MOD;
      a = a * a % MOD;
      b >>= 1;
    }
    return res;
  }
  public static long Power2(long a, long b)//i^N
  {
    long res = 1;
    while (b > 0)
    {
      if ((b & 1) != 0) res = res * a;
      a = a * a;
      b >>= 1;
    }
    return res;
  }
  public static long GCD(long a, long b)
  {
    if (a < b) return GCD(b, a);
    while (b != 0)
    {
      var r = a % b;
      a = b;
      b = r;
    }
    return a;
  }
  public static long LCM(long a, long b) => (b / GCD(a, b)) * a;
  public static long Comb(long n, long r, int MOD = 1000000007)
  {
    long ret = 1;
    long x = 1;
    for (long i = n; i >= n - r + 1; --i)
    {
      ret = ret / x * i;
      ret %= MOD;
      x++;
    }
    return ret;
  }
  public static long Comb2(long n, long r)
  {
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i)
    {
      Deno *= i;
      Nume *= n - i + 1;
    }
    return Nume / Deno;
  }
}
public static class Utils
{
  public static void Swap<T>(ref T A, ref T B)
  {
    T x = A;
    A = B;
    B = x;
  }
  public static int DigitSum(string N)
  {

    int ret = 0;
    for (int i = 0; i < N.Length; ++i) ret += N[i] - '0';
    return ret;
  }
}
class Program
{
  static void Main(string[] args)
  {
    var CompetitiveProgramming = new CompetitiveProgramming();
    CompetitiveProgramming.Solve();
  }
}
public static class io
{
  public static string Str => Console.ReadLine();
  public static string[] Strs => Str.Split(' ');
  public static long[] Longs => Strs.Select(long.Parse).ToArray();
  public static int[] Ints => Strs.Select(int.Parse).ToArray();
  public static char[] Chars => Str.ToArray();
  public static double[] Doubles => Strs.Select(double.Parse).ToArray();
  public static long Long1 => Longs[0];
  public static int Int1 => Ints[0];
  public static char Char1 => Chars[0];
  public static double Double1 => Doubles[0];
  public static long[] VerticalRead(int N) { long[] A = new long[N]; for (int i = 0; i < N; ++i) A[i] = Long1; return A; }
  public static void Write(string a) => Console.WriteLine(a);
  public static void Write(params object[] i) => Write(string.Join(" ", i));
  public static void Write<T>(IEnumerable<T> a) => Write(string.Join(" ", a));
  public static void Verticalwrite<T>(IEnumerable<T> a) { foreach (var z in a) Write(z); }
  public static void YN(bool i) { if (i) Write("Yes"); else Write("No"); }


  public static bool IsTypeEqual<T, U>() => typeof(T).Equals(typeof(U));
  public static T ConvertType<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
  public static T Cast<T>(string s)
  {
    if (IsTypeEqual<T, int>()) return ConvertType<T, int>(int.Parse(s));
    else if (IsTypeEqual<T, long>()) return ConvertType<T, long>(long.Parse(s));
    else if (IsTypeEqual<T, double>()) return ConvertType<T, double>(double.Parse(s));
    else if (IsTypeEqual<T, char>()) return ConvertType<T, char>(char.Parse(s));
    else return ConvertType<T, string>(s);
  }
  public static T Cin<T>() { var t = Strs; return (Cast<T>(t[0])); }
  public static (T, U) Cin<T, U>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1])); }
  public static (T, U, V) Cin<T, U, V>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2])); }
  public static (T, U, V, W) Cin<T, U, V, W>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2]), Cast<W>(t[3])); }
  public static (T, U, V, W, X) Cin<T, U, V, W, X>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2]), Cast<W>(t[3]), Cast<X>(t[4])); }
  public static (T, U, V, W, X, Y) Cin<T, U, V, W, X, Y>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2]), Cast<W>(t[3]), Cast<X>(t[4]), Cast<Y>(t[5])); }
  public static (T, U, V, W, X, Y, Z) Cin<T, U, V, W, X, Y, Z>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2]), Cast<W>(t[3]), Cast<X>(t[4]), Cast<Y>(t[5]), Cast<Z>(t[6])); }
}