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 1.8.0) (judge verdict: Runtime Error)

import java.util.*;

public class Main {

    public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
     	int num = sc.nextInt();
		int k = 1;
      	for(int i = 2; i < num; i++){
          k = k+i;
          if(num % k == 0){
          	System.out.println(k);
            break;
          }
        }
		
    }
}