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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        long N = Long.parseLong(in.nextLine());
        long p = 1;
        long k;
        while (true) {
            double D = Math.sqrt(1 + 8*p*N);
            String sqrt = String.valueOf(D);
            if (sqrt.charAt(sqrt.length()-1) == '0') {
                if ((D-1) % 2 == 0) {
                    k = (long) (D - 1) / 2;
                    break;
                }
            }
            p++;
        }
        System.out.println(k);
    }
}