We have a grid with (2^N - 1) rows and (2^M-1) columns. You are asked to write 0 or 1 in each of these squares. Let a_{i,j} be the number written in the square at the i-th row from the top and the j-th column from the left.

For a quadruple of integers (i_1, i_2, j_1, j_2) such that $1\leq i_1 \leq i_2\leq 2^N-1, 1\leq j_1 \leq j_2\leq 2^M-1$, let $S(i_1, i_2, j_1, j_2) = \displaystyle \sum_{r=i_1}^{i_2}\sum_{c=j_1}^{j_2}a_{r,c}.$ Then, let the oddness of the grid be the number of quadruples (i_1, i_2, j_1, j_2) such that S(i_1, i_2, j_1, j_2) is odd.

Find a way to fill in the grid that maximizes its oddness.

Constraints

• N and M are integers between 1 and 10 (inclusive).

Input

Input is given from Standard Input in the following format:

N M

Output

Print numbers to write in the grid so that its oddness is maximized, in the following format:

$a_{1,1}a_{1,2}\cdots a_{1,2^M-1}$
$a_{2,1}a_{2,2}\cdots a_{2,2^M-1}$
$\vdots$
$a_{2^N-1,1}a_{2^N-1,2}\cdots a_{2^N-1,2^M-1}$

If there are multiple solutions, you can print any of them.

Example

Input

1 2

Output

111

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