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

class program
{
    static public int mod = 1000000007;
    static void Main()
    {
        long[] abn = longa();
        long a = abn[0], b = abn[1], n = abn[2];
        if (n < b) Write(Floor(a * n / b*1m));
        else Write(Floor(a * (b - 1) / b*1m));
    }

    static int pow(int a, int b) { string binary = Convert.ToString(b, 2); int bileng = binary.Length; long a_power = a; long value = 1; for (int i = bileng - 1; i >= 0; i--) { if (binary[i] == '1') { value = value * a_power % mod; } a_power = a_power * a_power % mod; } return (int)value; }
    static string rstr() { return ReadLine(); }
    static int rint() { return int.Parse(ReadLine()); }
    static long rlong() { return long.Parse(ReadLine()); }
    static string[] stra() { return ReadLine().Split(' '); }
    static char[] chara() { string[] a = stra(); string b = ""; for (int i = 0; i < a.Length; i++) { b += a[i]; } return b.ToCharArray(); }
    static int[] inta() { string[] read_str_array = ReadLine().Split(' '); int[] return_int_array = new int[read_str_array.Length]; for (int countup_i = 0; countup_i < read_str_array.Length; countup_i++) { return_int_array[countup_i] = int.Parse(read_str_array[countup_i]); } return return_int_array; }
    static long[] longa() { string[] read_str_array = ReadLine().Split(' '); long[] return_long_array = new long[read_str_array.Length]; for (long countup_i = 0; countup_i < read_str_array.Length; countup_i++) { return_long_array[countup_i] = long.Parse(read_str_array[countup_i]); } return return_long_array; }
    static double[] doublea() { string[] read_str_array = ReadLine().Split(' '); double[] return_double_array = new double[read_str_array.Length]; for (long countup_i = 0; countup_i < read_str_array.Length; countup_i++) { return_double_array[countup_i] = double.Parse(read_str_array[countup_i]); } return return_double_array; }
    static long GCD(long a, long b) { if (a < b) { long temp = a; a = b; b = temp; } if (a % b == 0) { return b; } else { long temp = b; b = a % b; a = temp; return GCD(a, b); } }
    static long LCM(long a, long b) { return a * b / GCD(a, b); }
    static void WriteArray2(int[,] a, int b, int c) { for (int i = 0; i < b; i++) { for (int j = 0; j < c; j++) { if (j != 0) Write(" "); Write(a[i, j]); } WriteLine(); } }
    static void WriteArray(int[] a, int b) { for (int i = 0; i < b; i++) { Write(" "); Write(a[i]); } WriteLine(); }
}