Your task is to fill an n \times m grid using L-trominos (three squares that have an L-shape). For example, here is one way to fill a 4 \times 6 grid:

Input

The only input line has two integers n and m.

Output

Print n lines that each contain m letters between A–Z. Adjacent squares must have the same letter exactly when they belong to the same tromino.

You can print any valid solution. If there are no solutions, only print "IMPOSSIBLE".

Constraints

• 1 \le n,m \le 100

Example 1

Input:

4 6

Output:

AADDBB
ACCDEB
BCAEEC
BBAACC

Example 2

Input:

4 7

Output:

IMPOSSIBLE