Fill the grid

Given a $2^n \times 2^n$ grid, you are asked to fill it with L-shaped trominos except for a single cell (r, c). That one cell needs to be empty.

An L-shaped tromino is a figure obtained by removing a single cell from a $2 \times 2$ square.

In case it’s not possible to fill the grid, the program should print Impossible.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 9).

The second line contains the coordinates of the empty cell (r, c) (1 ≤ r, c ≤ $2^n$) where r is the row of the empty cell and c is the column.

Output

The program should print $2^n$ rows that contain $2^n$ numbers separated by a space. Each number should represent a single L-shaped tromino. The removed cell should be marked with a 0. The trominos should be indexed from 1 to $(2^{2n} - 1) / 3$. In case there are many solutions, the program can output any of those.

Examples