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 with AC Library v1.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#include<atcoder/all>
#define int long long
using namespace std;
using namespace atcoder;
int mn=10000000000000000;
void a(int x,int y){
  if(gcd(x,y)!=1)return;
  int A=inv_mod(x,y)*x;
  mn=min(mn,(A>1?A:A+x*y)-1);
}
signed main(){
  int N;
  cin>>N;
  N*=2;
  for(int i=1;i*i<=N;i++)
    if(N%i==0){
      a(i,N/i);
      a(N/i,i);
    }
  cout<<mn<<endl;
}