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 (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include<stdio.h>

int main(void){
  long long n;
  scanf("%lld",&n);
  long long i=1;
  if(n<=100){
  long long i=1;
  }else if(n<=1000){
  long long i=13;
  }else if(n<=5000){
  long long i=100;
  }else if(n<=10000){
  long long i=140;
  }else if(n<=100000){
  long long i=445;
  }else{
    long long i=1100140;
  }
  
  while((i*(i+1)/2)%n!=0){
    i++;
  }
  printf("%lld",i);
  return 0;
}