Position-Parity Grid

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given an $r$-by-$c$ grid with 1-based indices, print 1 at $(i,j)$ when $i+j$ is even; otherwise print 0. Output $r$ rows of exactly $c$ adjacent characters with no spaces.

Input

One line contains $r$ and $c$ in this order.

Output

Print the grid as described.

Subtasks

• Subtask 1 (20%): $1\le r,c\le 5$.

• Subtask 2 (30%): $1\le r,c\le 15$.

• Subtask 3 (50%): $1\le r,c\le 30$.

Examples

Example 1

Input:

2 3

Output:

101
010

Explanation:

There are 2 rows and 3 columns. Cell (1,1) is 1, and parity alternates along rows and columns.

Example 2

Input:

1 1

Output:

1

Explanation:

There are 1 rows and 1 columns. Cell (1,1) is 1, and parity alternates along rows and columns.