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.