nth Rational number in Calkin-Wilf sequence

What is Calkin Wilf Sequence? 
A Calkin-Wilf tree (or sequence) is a special binary tree which is obtained by starting with the fraction 1/1 and adding a/(a+b) and (a+b)/b iteratively below each fraction a/b. This tree generates every positive rational number. Writing out the terms in a sequence gives 1/1, 1/2, 2/1, 1/3, 3/2, 2/3, 3/1, 1/4, 4/3, 3/5, 5/2, 2/5, 5/3, 3/4, 4/1, ...The sequence has the property that each denominator is the next numerator.

The image above is the Calkin-Wilf Tree where all the rational numbers are listed. The children of a node a/b is calculated as a/(a+b) and (a+b)/b.
The task is to find the nth rational number in breadth first traversal of this tree. 

Examples: 

Input : 13
Output : [5, 3]

Input : 5
Output : [3, 2]

Explanation: 

This tree is a Perfect Binary Search tree and we need floor(log(n)) steps to compute nth rational number. The concept is similar to searching in a binary search tree. Given n we keep dividing it by 2 until we get 0. We return fraction at each stage in the following manner:

    if n%2 == 0
        update frac[1]+=frac[0]
    else
        update frac[0]+=frac[1]

Below is the program to find the nth number in Calkin Wilf sequence:

// C++ program to find the 
// nth number in Calkin
// Wilf sequence:
# include<bits/stdc++.h>
using namespace std;

int frac[] = {0, 1};

// returns 1x2 int array  
// which contains the nth
// rational number
int nthRational(int n)
{
    if (n > 0)
        nthRational(n / 2);

    // ~n&1 is equivalent to 
    // !n%2?1:0 and n&1 is 
    // equivalent to n%2
    frac[~n & 1] += frac[n & 1];
}

// Driver Code
int main()
{
    int n = 13; // testing for n=13
    
    // converting array 
    // to string format
    nthRational(n);
    cout << "[" << frac[0] << "," 
         << frac[1] << "]" << endl;
    return 0;
}

// This code is contributed
// by Harshit Saini

// Java program to find the nth number
// in Calkin Wilf sequence:
import java.util.*;

public class GFG {
    static int[] frac = { 0, 1 };

    public static void main(String args[])
    {
        int n = 13; // testing for n=13

        // converting array to string format
        System.out.println(Arrays.toString(nthRational(n)));
    }

    // returns 1x2 int array which 
    // contains the nth rational number
    static int[] nthRational(int n)
    {
        if (n > 0)
            nthRational(n / 2);

        // ~n&1 is equivalent to !n%2?1:0 
        // and n&1 is equivalent to n%2
        frac[~n & 1] += frac[n & 1];
        

        return frac;
    }
}

# Python program to find 
# the nth number in Calkin
# Wilf sequence:
frac = [0, 1]

# returns 1x2 int array 
# which contains the nth
# rational number
def nthRational(n):
    if n > 0:
        nthRational(int(n / 2))
    
    # ~n&1 is equivalent to 
    # !n%2?1:0 and n&1 is 
    # equivalent to n%2
    frac[~n & 1] += frac[n & 1]
    
    return frac

# Driver code
if __name__ == "__main__":
    
    n = 13 # testing for n=13
    
    # converting array 
    # to string format
    print(nthRational(n))
    
# This code is contributed
# by Harshit Saini

// C# program to find the nth number 
// in Calkin Wilf sequence: 
using System;

class GFG
{ 
    static int[] frac = { 0, 1 }; 

    public static void Main(String []args) 
    { 
        int n = 13; // testing for n=13 

        // converting array to string format 
        Console.WriteLine("[" + String.Join(",", 
                                nthRational(n)) + "]"); 
    } 

    // returns 1x2 int array which 
    // contains the nth rational number 
    static int[] nthRational(int n) 
    { 
        if (n > 0) 
            nthRational(n / 2); 

        // ~n&1 is equivalent to !n%2?1:0 
        // and n&1 is equivalent to n%2 
        frac[~n & 1] += frac[n & 1]; 
        
        return frac; 
    } 
}

// This code is contributed by 29AjayKumar

<script>
// Javascript program to find the nth number
// in Calkin Wilf sequence:
let frac = [0, 1];

let n = 13; // testing for n=13

// converting array to string format
document.write(`[${nthRational(n)}]`)

// returns 1x2 int array which
// contains the nth rational number
function nthRational(n) {
    if (n > 0)
        nthRational(Math.floor(n / 2));

    // ~n&1 is equivalent to !n%2?1:0
    // and n&1 is equivalent to n%2
    frac[~n & 1] += frac[n & 1];
    return frac;
}

// This code is contributed by _saurabh_jaiswal

</script>

[5,3]

Time complexity : O(log(n))

Auxiliary Space : O(1)

Explanation: 
For n = 13,