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 Scala (2.13.1) (judge verdict: Time Limit Exceeded)

object Main {
  def main(args: Array[String]) = {
  val N = io.StdIn.readLong
  var sum = 0L
  var k = 1
  while(true) {
    sum += k
    if(sum % N == 0) {
      println(k)
      System.exit(0)
    }
    k += 1
  }
  }
}