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>

long long int f(long long int n)
{
    long long int tmpt = n, tmp = n / 2;
while (1)
{
    if (tmp * tmp == n)
        return (tmp);
    if (tmp * tmp > n)
    {
        if ((tmp - 1) * (tmp - 1) < n)
            return (0);
        tmpt = tmp;
        tmp /= 2;
    }
    else
    {
        if ((tmp + 1) * (tmp + 1) > n)
            return (0);
        tmp = (tmpt + tmp) / 2;
    }
}
    
}

int main(void){
    // Your code here!
    long long int n, a, ans, tmp;
    
    scanf("%lld", &n);
    a = 1;
    while (1)
    {
        if (f(1 + 8 * a * n))
        {
            printf("%lld", (f(1 + 8 * a * n) - 1) / 2);
            return (0);
        }
        a++;
        
    }
}