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 Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

N = gets.to_i
i = 0
while true do
    i++
    l = 1
    r = 10000000000;
    while r - l > 1
        e = (l + r) / 2
        num = e * (e + 1) / 2
        if N * i < num
            l = e
        else
            r = e
        end
    end
    if(num == i * N)
        puts e
        exit
    end
end