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 C++ (Clang 10.0.0 with AC Library v1.1) (judge verdict: Time Limit Exceeded)

#include <iostream>
using namespace std;
int main(void){
    int k=1, i=0, N;
    cin >> N;
    while(true){
        if(k < N){
            k += i+2;
          	i++;
            continue;
        } 
        k %= N;
        if(k % N == 0){
            printf("%d",i+1);
            break;
        } else {
            k += i+2;
          	i++;
        }
    }
}