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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

long long kirui[100010] = {};
long long gurui[100010] = {};
vector<long long> vec;
int main(){
    long long n;
    cin >> n;

    long long tmp = 1;

    int i = 0;
    while(llabs(tmp) <= 10e15){
        if(tmp > 0){
            kirui[i+1] = tmp;
        }else{
            gurui[i+1] = tmp;
        }
        kirui[i+1] += kirui[i];
        gurui[i+1] += gurui[i];

        vec.push_back(tmp);
        tmp *= -2;
        i++;
    }

    if(n == 0){
        cout << 0 << endl;
        return 0;
    }

    string ans = "";
    for(int i = vec.size()-1;i >= 0;i--){
        if(gurui[i] <= n-vec[i] && n-vec[i] <= kirui[i]){
            n-=vec[i];
            ans = ans+"1";
        }else{
            if(ans != ""){
                ans += "0";
            }
        }
    }

    cout << ans << endl;

    return 0;
}