Problem:
Score : 400 points

Problem Statement

Give a pair of integers (A, B) such that A^5-B^5 = X.
It is guaranteed that there exists such a pair for the given integer X.

Constraints

1 \leq X \leq 10^9

X is an integer.

There exists a pair of integers (A, B) satisfying the condition in Problem Statement.

Input

Input is given from Standard Input in the following format:

X

Output

Print A and B, with space in between.
If there are multiple pairs of integers (A, B) satisfying the condition, you may print any of them.

A B

Sample Input 1

33

Sample Output 1

2 -1

For A=2 and B=-1, A^5-B^5 = 33.

Sample Input 2

1

Sample Output 2

0 -1

Solution in Rust (1.42.0) (judge verdict: Accepted)

fn main() {
    ioset! { inp, buf }
    macro_rules! scan {
        ($($r:tt)*) => {
            input! { inp, $($r)* }
        }
    }
    macro_rules! print {
        ($($t:expr),*) => {
            write!(buf, $($t),*).unwrap();
        } 
    }
    scan! { X: u64, }

    let mut vec = vec![0u64, 1];
    while vec[vec.len() - 1] - vec[vec.len() - 2] < 1e9 as u64 {
        let i = vec.len() as u64;
        vec.push(i * i * i * i * i);
    }

    for i in 0..vec.len() {
        for j in i..vec.len() {
            if vec[j] - vec[i] == X {
                println!("{} {}\n", j, i);
                return;
            }
            if vec[j] + vec[i] == X {
                println!("{} {}\n", i, -(j as isize));
                return;
            }
        }
    }
    println!("-1\n");
}

pub trait ToVec {
    type Item;
    fn tovec(self) -> Vec<Self::Item>;
}

impl<I: std::iter::Iterator> ToVec for I {
    type Item = <Self as std::iter::Iterator>::Item;
    fn tovec(self) -> Vec<Self::Item> {
        self.collect::<Vec<Self::Item>>()
    }
}

/* I/O */

use std::io::{ stdout, BufWriter, Write };

#[macro_export]
macro_rules! ioset {
    ($inp:ident, $buf:ident) => {
        inset!($inp);
        outset!($buf);
    }
}

#[macro_export]
macro_rules! inset {
    (source = $s:expr, $iter:ident) => {
        let mut $iter = $s.split_whitespace();
    };
    ($iter:ident) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut $iter = s.split_whitespace();
    }
}

#[macro_export]
macro_rules! input {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt, $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input! { $iter, $($r)* }
    };
    ($iter:expr, mut $var:ident : $t:tt, $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input! { $iter, $($r)* }
    };
    ($iter:expr, ($var:expr) : $t:tt, $($r:tt)*) => {
        $var = read_value!($iter, $t);
        input! { $iter, $($r)* }
    };
}

#[macro_export]
macro_rules! read_value {

    // tuple
    ($iter:expr, ( $($t:tt), * )) => {
        ( $(read_value!($iter, $t)), * )
    };
    
    // array
    ($iter:expr, [ $t:tt; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    
    // string
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    
    // any other
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

#[macro_export]
macro_rules! outset {
    ($buf:ident) => {
        let sout = stdout();
        let mut $buf = BufWriter::new(sout.lock());
    }
}

#[macro_export]
macro_rules! output {
    ($buf:expr, $($t:expr),*) => {
        write!($buf, $($t),*).unwrap();
    }
}

struct Chars<'a>(&'a Vec<char>);

impl<'a> std::fmt::Display for Chars<'a> {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> Result<(), std::fmt::Error> {
        write!(f, "{}", self.0.iter().collect::<String>())
    }
}

use std::cmp::Ordering;

pub trait BinarySearch<T> {
    fn lower_bound(&self, x: &T) -> usize;
    fn upper_bound(&self, x: &T) -> usize;
}

impl<T: Ord> BinarySearch<T> for [T] {
    fn lower_bound(&self, x: &T) -> usize {
        let mut ng = -1i64;
        let mut ok = self.len() as i64;
        while ok - ng > 1 {
            let m = (ok + ng) / 2;
            match self[m as usize].cmp(x) {
                Ordering::Greater | Ordering::Equal => {
                    ok = m;
                }
                _ => {
                    ng = m;
                }
            }
        }
        ok as usize
    }
    fn upper_bound(&self, x: &T) -> usize {
        let mut ng = -1i64;
        let mut ok = self.len() as i64;
        while ok - ng > 1 {
            let m = (ok + ng) / 2;
            match self[m as usize].cmp(x) {
                Ordering::Greater => {
                    ok = m;
                }
                _ => {
                    ng = m;
                }
            }
        }
        ok as usize
    }
}