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 Rust (1.42.0) (judge verdict: Wrong Answer)

#[allow(dead_code)]
fn main() {
    let stdin = stdin();
    solve(StdinReader::new(stdin.lock()));
}

pub fn solve<R: BufRead>(mut reader: StdinReader<R>) {
    let n = reader.u();

    let mut d = HashMap::new();
    let mut l = 2;
    let mut k = n;
    while l * l <= k {
        if k % l != 0 {
            l += 1;
        } else {
            *d.entry(l).or_insert(0) += 1;
            k /= l;
        }
    }
    *d.entry(k).or_insert(0) += 1;
    *d.entry(2).or_insert(0) += 1; // 2nm = k(k+1)を作る

    let mut m = Vec::new();
    for (&p, &c) in &d {
        let mut l = 1;
        for _ in 0..c {
            l *= p;
        }
        m.push(l);
    }

    //bit全探索する
    let p = 1 << d.len();
    let mut ans = std::usize::MAX;
    for i in 0..p {
        let mut a = vec![1, 1];
        //片側に全部入れる
        for j in 0..d.len() {
            a[if i >> j & 1 == 1 { 0 } else { 1 }] *= m[j];
        }
        a.sort();

        ans = min(ans, sol(a[1], a[0]));
    }
    println!("{}", ans);
}

fn sol(large: usize, small: usize) -> usize {
    if small == 1 {
        return large - 1;
    }
    let a = div(1, large, small) * large - 1;
    let b = div(large - 1, small, large) * large;
    min(a, b)
}

pub fn div(p: usize, e: usize, m: usize) -> usize {
    p * pow(e % m, m - 2, m) % m
}
pub fn pow(p: usize, e: usize, m: usize) -> usize {
    let mut result = 1;
    let mut cur = p;
    let mut e = e;
    while e > 0 {
        if e & 1 == 1 {
            result = (cur * result) % m;
        }
        e >>= 1;
        cur = cur * cur % m;
    }
    result
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn run() {
        assert_eq!(div(2, 5, 7), 6);
        assert_eq!(pow(5, 4, 500), 125);
    }
}

#[allow(unused_imports)]
use itertools::Itertools;
#[allow(unused_imports)]
use std::{cmp::*, collections::*, io::*, num::*, str::*};
#[allow(unused_imports)]
use stdin_reader::StdinReader;

#[allow(dead_code)]
pub mod stdin_reader {
    use std::{fmt::Debug, io::*, str::*};

    pub struct StdinReader<R: BufRead> {
        reader: R,
        buf: Vec<u8>,
        // Should never be empty
        pos: usize, // Should never be out of bounds as long as the input ends with '\n'
    }

    impl<R: BufRead> StdinReader<R> {
        pub fn new(reader: R) -> StdinReader<R> {
            let (buf, pos) = (Vec::new(), 0);
            StdinReader { reader, buf, pos }
        }

        pub fn n<T: FromStr>(&mut self) -> T
        where
            T::Err: Debug,
        {
            if self.buf.is_empty() {
                self._read_next_line();
            }
            let mut start = None;
            while self.pos != self.buf.len() {
                match (self.buf[self.pos], start.is_some()) {
                    (b' ', true) | (b'\n', true) => break,
                    (_, true) | (b' ', false) => self.pos += 1,
                    (b'\n', false) => self._read_next_line(),
                    (_, false) => start = Some(self.pos),
                }
            }
            match start {
                Some(s) => from_utf8(&self.buf[s..self.pos]).unwrap().parse().unwrap(),
                None => panic!("入力された数を超えた読み込みが発生しています"),
            }
        }

        fn _read_next_line(&mut self) {
            self.pos = 0;
            self.buf.clear();
            if self.reader.read_until(b'\n', &mut self.buf).unwrap() == 0 {
                panic!("Reached EOF");
            }
        }

        pub fn str(&mut self) -> String {
            self.n()
        }
        pub fn s(&mut self) -> Vec<char> {
            self.n::<String>().chars().collect()
        }
        pub fn i(&mut self) -> i64 {
            self.n()
        }
        pub fn i2(&mut self) -> (i64, i64) {
            (self.n(), self.n())
        }
        pub fn i3(&mut self) -> (i64, i64, i64) {
            (self.n(), self.n(), self.n())
        }
        pub fn u(&mut self) -> usize {
            self.n()
        }
        pub fn u2(&mut self) -> (usize, usize) {
            (self.n(), self.n())
        }
        pub fn u3(&mut self) -> (usize, usize, usize) {
            (self.n(), self.n(), self.n())
        }
        pub fn u4(&mut self) -> (usize, usize, usize, usize) {
            (self.n(), self.n(), self.n(), self.n())
        }
        pub fn u5(&mut self) -> (usize, usize, usize, usize, usize) {
            (self.n(), self.n(), self.n(), self.n(), self.n())
        }
        pub fn u6(&mut self) -> (usize, usize, usize, usize, usize, usize) {
            (self.n(), self.n(), self.n(), self.n(), self.n(), self.n())
        }
        pub fn f(&mut self) -> f64 {
            self.n()
        }
        pub fn f2(&mut self) -> (f64, f64) {
            (self.n(), self.n())
        }
        pub fn c(&mut self) -> char {
            self.n::<String>().pop().unwrap()
        }
        pub fn iv(&mut self, n: usize) -> Vec<i64> {
            (0..n).map(|_| self.i()).collect()
        }
        pub fn iv2(&mut self, n: usize) -> Vec<(i64, i64)> {
            (0..n).map(|_| self.i2()).collect()
        }
        pub fn iv3(&mut self, n: usize) -> Vec<(i64, i64, i64)> {
            (0..n).map(|_| self.i3()).collect()
        }
        pub fn uv(&mut self, n: usize) -> Vec<usize> {
            (0..n).map(|_| self.u()).collect()
        }
        pub fn uv2(&mut self, n: usize) -> Vec<(usize, usize)> {
            (0..n).map(|_| self.u2()).collect()
        }
        pub fn uv3(&mut self, n: usize) -> Vec<(usize, usize, usize)> {
            (0..n).map(|_| self.u3()).collect()
        }
        pub fn uv4(&mut self, n: usize) -> Vec<(usize, usize, usize, usize)> {
            (0..n).map(|_| self.u4()).collect()
        }
        pub fn fv(&mut self, n: usize) -> Vec<f64> {
            (0..n).map(|_| self.f()).collect()
        }
        pub fn cmap(&mut self, h: usize) -> Vec<Vec<char>> {
            (0..h).map(|_| self.s()).collect()
        }
    }
}