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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define int long long
typedef pair<int,int> P;
int INF = 1e19+7;
int mod = 998244353;
int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};
signed main() {
    int N;
    cin >> N;
    int ans = N-1;
    for(int i = 1; i*N <= INF && N*N >= i*N; i++) {
        int cnt = sqrt(i*N);
        if(cnt*(cnt-1)/2%N == 0) {
            ans = min(ans,cnt);
        }
        if((cnt+1)*cnt/2%N == 0) {
            ans = min(ans,cnt);
        }
    }
    cout << ans << endl;
}