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>
#include <math.h>
int main(void){
    long long n,k,sum=0;
    
    if(scanf("%lld",&n)==1);
    
    for(k=1;;k++){
        /*sum+=k;
        if(sum%n==0){
            break;
        }*/
        if(ceil((0.5*k*(k+1)/n))==floor((0.5*k*(k+1)/n))){
            break;
        }
    }
    printf("%lld",k);
    
    return 0;
}