Problem:
Score : 300 points

Problem Statement

Given an integer N, find the base -2 representation of N.

Here, S is the base -2 representation of N when the following are all satisfied:

S is a string consisting of 0 and 1.

Unless S = 0, the initial character of S is 1.

Let S = S_k S_{k-1} ... S_0, then S_0 \times (-2)^0 + S_1 \times (-2)^1 + ... + S_k \times (-2)^k = N.

It can be proved that, for any integer M, the base -2 representation of M is uniquely determined.

Constraints

Every value in input is integer.

-10^9 \leq N \leq 10^9

Input

Input is given from Standard Input in the following format:

N

Output

Print the base -2 representation of N.

Sample Input 1

-9

Sample Output 1

1011

As (-2)^0 + (-2)^1 + (-2)^3 = 1 + (-2) + (-8) = -9, 1011 is the base -2 representation of -9.

Sample Input 2

123456789

Sample Output 2

11000101011001101110100010101

Sample Input 3

0

Sample Output 3

0

Solution in Kotlin (1.0.0) (judge verdict: Runtime Error)

import java.util.Scanner

fun pow(a:Int, b:Int): Int{
	var p: Int = 1

	if(b <= 0) p = 1
	else{
		for(i in 1..b) p *= a
	}

	return p
}

fun main(args: Array<String>){
	val s = Scanner(System.`in`).nextLine()
	val N = Integer.parseInt(s)

	var n: Int = N
	var i: Int = 1
	var str: String = ""

	while(n != 0){
		if(n % pow(2,i) == 0){
			str += "0"
		}
		else{
			str += "1"
			n += (pow(-1,i) * pow(2,i-1)).toInt()
		}
		i++
	}

	if(N == 0) println("0")
	else println(str.reversed())
}