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.Linq;

namespace ConsoleApp1 {
    public class Class1 {
        static void Main(string[] args) {
            var num = Console.ReadLine().Trim().Split(' ').Select(_ => long.Parse(_)).ToArray();
            var A = num[0];
            var B = num[1];
            var N = num[2];
            var mn = 0;
            var mx = N;
            var max = 0;
            var tmp = 0;

            while (true) {
                tmp = (int)Math.Floor(mn + (mx - mn) / 2f);
                max = Test(tmp, A, B);
                if (max < Test(tmp + 1, A, B)) {
                    max = Test(tmp + 1, A, B);
                    mn = tmp;
                    if(mn + 1 == mx) {
                        break;
                    }
                } else if (max < Test(tmp - 1, A, B)) {
                    max = Test(tmp - 1, A, B);
                    mx = tmp;
                    if(mx == mn) {
                        break;
                    }
                } else {
                    break;
                }
            }

            Console.Write(max);
            Console.Read();
        }

        static int Test(int x, float A, float B) {
            var n = Math.Floor(A * x / B) - A * Math.Floor(x / B);
            return (int)n;
        }
    }
}