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 Python (3.8.2) (judge verdict: Wrong Answer)

N = int(input())
x = 1

import math as m
import decimal as d
N = d.Decimal(N)
while x < N:
  target = N*x
  a = m.floor(m.sqrt(target*2))
  check = a*(a+1)/2
  #print(check,target)
  if check == target:
    print(a)
    exit(0)
  x += 1