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 Ruby (2.3.3) (judge verdict: Runtime Error)

args = gets.split(" ")
n = args[0].to_i
m = args[1].to_i
#p n
#p m

$candies = gets.split(" ").map!{|x|x.to_i}
#p $candies

def calc_sum(l,r)
	#printf("%d,%d\n",l,r)
	sum = 0
	i = l
	loop do
		sum = sum + $candies[i]
		i=i+1
		if( i > r ) then
			#p 'break'
			break
		end
	end
	return sum
end

count = 0

for r in 0..n-1
	for l in 0..r
		sum = calc_sum(l,r)
		#p sum
		if(sum%m==0)
			count= count+1
		end
	end
end

p count