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()
{
  unsigned long long n,i,k,sum;
  
  (void) scanf("%llu",&n);
  
  k=1;
  sum = 0;
  while(1)
  {
    sum+=k;
    //printf("k=%llu sum=%llu\n",k,sum);
    if ( sum % n == 0 )
    {
    printf("%llu",k);
      return 0;
    }
    k+=1;
    
  }
  return 0;
}