Pal like board games. One day Shark shows him a new board game. This is different from other board games .It follows some rules .

It consists of two characters "." and "#". (Without quotes).

No two adjacent characters in a horizontal or vertical line should be same.

Lower left corner of board is "." ( Without quotes).

If there exists no such board for values of n and m print "Not Exists"(quotes for clarity). else print possible configuration of board. Now pal wants your help to solve this task.

Input

Single line of input contain value of n and m.

Output

Print possible configuration of board if possible or print "not exists".

Limits

1<=n<=3000

1<=m<=2000

NOTE- matrix must contain both '.' and '#'.