E - Odd Sum Rectangles /

問題文

(2^N - 1)(2^M-1) 列のグリッドがあり、 あなたはこれからすべてのマスに 0, 1 のいずれかの数字を書き込みます。 上から i 行目、左から j 列目に書き込む数字を a_{i,j} とします。

1\leq i_1 \leq i_2\leq 2^N-1, 1\leq j_1 \leq j_2\leq 2^M-1 をみたす整数の組 (i_1, i_2, j_1, j_2) に対し、 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} と定義し、 さらに、グリッドの「奇妙さ」を S(i_1, i_2, j_1, j_2) が奇数となるような (i_1, i_2, j_1, j_2) の個数 と定義します。

制約

• N, M1 以上 10 以下の整数

入力

N M


出力

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}


入力例 1

1 2


出力例 1

111


S(1, 1, 1, 1)S(1, 1, 2, 2)S(1, 1, 3, 3)S(1, 1, 1, 3) が奇数となるため、このグリッドの奇妙さは 4 です。

Score : 900 points

Problem Statement

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.

Sample Input 1

1 2


Sample Output 1

111


For this grid, S(1, 1, 1, 1), S(1, 1, 2, 2), S(1, 1, 3, 3), and S(1, 1, 1, 3) are odd, so it has the oddness of 4.

We cannot make the oddness 5 or higher, so this is one of the ways that maximize the oddness.