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: Wrong Answer)

#include<cstdio>
#include<bits/stdc++.h>
typedef long long int ll;
#define REP(i, n) for(int i = 0; i < (n); i++)
#define FOR_IN(i, a, b) for(int i = (a); i < (b); i++)
#define BETWEEN(x, a, b) ((x) >= (a) && (x) <= (b))
#define BIT(b, i) (((b) >> (i)) & 1)
#define LOG_F 1
#define LOG(...) if(LOG_F) fprintf(stderr, __VA_ARGS__)

using namespace std;

ll pow(int x, int n){
  return n == 0 ? 1 : x * pow(x, n - 1);
}

int sign(int x){
  return x>=0 ? 1 : -1;
}
/*

 */
int n;
vector<int> ks;

int main(){
  cin>>n;

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

  while(abs(n)>0){
    LOG("n=%d, ",n);
    int s = n>0 ? 1 : 0;
    int k=0;
    for(; pow(2, 2 * k + s) <= abs(n); k++);
    k--;
    int l = 2 * k + s + 1;
    LOG("l=%d\n",l);
    
    ks.push_back(l);
    n -= pow(-2, l);
  }

  ks.push_back(-1);

  // for(auto k : ks){
  //   LOG("%d\n", k);
  // }

  if(ks.empty()){
    cout<<0<<endl;
  } else {
    for(int i=0; i<ks.size()-1; i++){
      cout<<1;
      REP(j,ks[i]-ks[i+1]-1){
        cout<<0;
      }
    }
    cout<<endl;
  }
  
  return 0;
}