Rooks inside a rectangle P31389

Consider a rectangular board $r \times c$ with $r \le c$. Write a program that prints all the ways to place $r$ rooks on the board so that no rook threatens another rook.

Input

Input consists of two natural numbers $r$ and $c$, with $1 \le r \le c$.

Output

Print all the ways to place $r$ rooks on the board so that no rook threatens another rook. Represent the rooks with a ‘R’, and the empty positions with a dot. Print an empty line after each board.

Information about the checker

You can print the solutions to this exercise in any order.