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 (GCC 5.4.1) (judge verdict: Accepted)

#include <malloc.h>
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>

//ABC105C
int main(void) {
  long long bit[100], n, k=2, i, cou=0, tmp=1, flag=0;
  scanf("%lld", &n);

  for(i=0; i<33; i++)
    bit[i]=0;

  if(n>0){
    if(n%2==1) bit[0]=1;
    for(i=1; i<16; i++){
      k*=2;
      n-=tmp, tmp*=4;
      if(n<=0) break;
      bit[2*i-1]=(n-1)%k>=(k/2) ? 0 : 1;
      k*=2;
      bit[2*i]=(n-1)%k>=(k/2) ? 0 : 1;
    }
  }else if(n<0){
    n*=-1;
    tmp=2;
    for(i=0; i<16; i++){
      //printf("i=%lld n=%lld k=%lld\n", i, n, k);
      bit[2*i]=(n-1)%k>=(k/2) ? 0 : 1;
      k*=2;
      bit[2*i+1]=(n-1)%k>=(k/2) ? 0 : 1;
      k*=2;
      n-=tmp, tmp*=4;
      if(n<=0) break;
    }
  }else{
    printf("0");
    return 0;;
  }

  for(i=32; i>=0; i--){
    if(flag==0&&bit[i]==0) continue;
    else{
      flag=1;
      printf("%lld", bit[i]);
    }
  }
  return 0;
}