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 Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"fmt"
	"math"
)

func main() {
	// Code for B - Sum is Multiple
	var N float64
	fmt.Scan(&N)

	var a float64 = 1
	var b float64
	var c float64

	for {
		b = math.Sqrt(1.0 + 8.0*a*N)
		c = b - math.Floor(b)
		//if math.Floor(b) == b {
		if c == 0 {
			//fmt.Println(int(b))
			if int(b)%2 != 0 {
				fmt.Println(int(int(b-1) / 2))
				break
			}
		}
		a++
	}
}