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: Accepted)

import java.util.BitSet

fun main(args: Array<String>) {
    var N = readInputLine().toLong()
    
    if (N == 0L) {
        println(0)
        return
    }
    
    val ans = BitSet()
    
    var base = -2L
    
    for (i in 0..60) {
        if (N % base != 0L) {
            ans.set(i)
            N -= base / -2L
        }
        base *= -2L
    }
    
    val ansStr = CharArray(ans.size(), {'0'})
    
    for (i in 0 until ans.size()) {
        if (ans.get(i)) {
            ansStr[ans.size() - i - 1] = '1'
        }
    } 
    
    println(ansStr.joinToString("").trimStart{it == '0'})
}

fun readInputLine(): String {
    return readLine()!!
}