You are working as a cryptographer in a post-apocalyptic world. The most common form of information is transmitted in messages with cyclic arrays of size ~N~ where each element is either ~1~ or ~-1~, taking inspiration from the previously failed binary system. To ensure that the message is not corrupted, the receiver of the message uses an identification number ~K~. The message can be verified if the sum of the products of elements in every cyclic subarray of length ~K~ is ~0~. You would like to send a valid message to a recipient with identification number ~K~. Please find any valid message that can be verified, or determine that no such message exists.

Constraints

~1 \le K \le N \le 2^{21}~

Subtask 1 [5%]

~1 \le K \le N \le 2^4~

Subtask 2 [15%]

~1 \le K \le N \le 2^{11}~

Subtask 3 [20%]

If ~N~ and ~K~ are expressed as ~2^a \times x~ and ~2^b \times y~ respectively where ~x~ and ~y~ are odd and ~a~ and ~b~ are integers, then ~a > b~.

Subtask 4 [60%]

No additional constraints.

Input Specification

The first and only line contains ~2~ integers ~N~ and ~K~, as specified in the problem statement.

Output Specification

If it is impossible to create a valid message, output 0. Otherwise, output ~N~ space-separated integers (either ~1~ or ~-1~) on a single line, representing the cyclic array.

Note: your output must follow the standard convention of not having any leading or trailing whitespace, and it must end with a new line.

Sample Input

8 3

Sample Output

-1 -1 1 1 -1 1 -1 1

Explanation

The diagram below shows the cyclic array, with the indices labeled below the elements.

The following list shows the product of every cyclic subarray of length ~K~:

The product of elements from index ~1~ to ~3~ is ~1~.
The product of elements from index ~2~ to ~4~ is ~-1~.
The product of elements from index ~3~ to ~5~ is ~-1~.
The product of elements from index ~4~ to ~6~ is ~-1~.
The product of elements from index ~5~ to ~7~ is ~1~.
The product of elements from index ~6~ to ~8~ is ~-1~.
The product of elements from index ~7~ to ~1~ is ~1~.
The product of elements from index ~8~ to ~2~ is ~1~.

Summing, we get ~1-1-1-1+1-1+1+1 = 0~, so this message can be verified. Note that this is not the only possible solution, and other verifiable messages will also be accepted.