J. Lampshade
time limit per test
2.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Hacker Kirill watched too many videos on youtube and decided to do needlework. His choice fell on a table lamp – it was decided to make creative decoration. A lampshade made of beads was chosen as a decoration. Individual beads are strung on threads, and the threads are fixed parallel to each other in between two round holders.

The lampshade consists of $$$n$$$ parallel threads. All threads have the same length, and exactly $$$k$$$ beads fit on them. The beads on the threads are placed as tightly as possible, and the threads are fixed in the same way, so the first beads are next to the first beads of neighboring threads, and the $$$k$$$-th beads are next to the $$$k$$$–th ones.

Kirill has beads in two colors – black and white. By changing their position on the threads and the order of the threads themselves, you can get different patterns. Kirill decided to design the lampshade so that two adjacent threads differed from each other in the color of exactly one bead, and there were no two identical threads.

Write a program that helps Kirill to create a scheme of a lampshade from $$$n$$$ threads, having $$$k$$$ beads on each thread, or it should inform that such a scheme does not exist.

Note since the lampshade is attached to the lamp with only one holder, the threads have a beginning, and the threads that are a reflection of each other are different. For example, the threads «BWBW» and «WBWB» are different, although the first one can be made from the second one backwards.

Input

The input consists of two integer numbers $$$ n $$$ $$$( 2 \leq n \leq 10^4 )$$$ and $$$ k $$$ $$$( 2log_{2}n \leq k \leq 100 )$$$, separated by a space.

Output

If there is no solution, the program should output the phrase «No solution» (without quotes).

If a solution exists, the output consists of $$$n$$$ lines of $$$k$$$ characters. Each line describes one thread of the lampshade in the order of adjacency. The first thread is considered adjacent not only to the second but also to the last.

White beads are indicated by a capital Latin «W», and black beads are indicated by a capital «B».

If there are multiple solutions, print any of them.

Example
Input
6 6
Output
BWWWWW
BBWWWW
WBWWWW
WBBWWW
BBBWWW
BWBWWW