Problem:
Score : 600 points

Problem Statement

Given is an integer N.
Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N.
It can be proved that such a positive integer k always exists.

Constraints

1 \leq N \leq 10^{15}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer in a line.

Sample Input 1

11

Sample Output 1

10

1+2+\cdots+10=55 holds and 55 is indeed a multple of N=11.
There are no positive integers k \leq 9 that satisfy the condition, so the answer is k = 10.

Sample Input 2

20200920

Sample Output 2

1100144

Solution in C# (.NET Core 3.1.201) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Runtime.InteropServices.ComTypes;

namespace ConsoleApp2
{
    class Program
    {
        static void Main()
        {

            int input = int.Parse(Console.ReadLine());

            long sum = 0;
            for (int i = 1; i < input; i++)
            {
                sum += i;
                if (sum % input ==0)
                {
                    Console.WriteLine(i);
                    break;
                }
            }
        }
    }
}