Problem Description

For her birthday, Ksonia received an infinite chessboard, where each cell is colored either black or white. She wants to cut out a connected shape from it, but the shape must contain exactly $b$ black cells and $w$ white cells. The shape does not need to be fully filled, but it must be connected.

:::align{center}

An example of a valid shape. The unfilled cells in the middle do not matter; the key is that the shape must be connected. This shape has four white cells and four black cells. :::

:::align{center}

An example of an invalid shape because it is not connected. :::

Please help Ksonia find any such shape, or state that it does not exist.

Input Format

The first line contains two integers $w$ and $b$ ($0 \leq w, b \leq 100$), representing the numbers of white cells and black cells, respectively.

Output Format

If no solution exists, output a single number $-1$.

Otherwise, output two integers $n$ and $m$ ($1 \leq n, m \leq 250$) in the first line, the size of the rectangular region containing the required shape. It can be proven that if a solution exists, then there is a solution that satisfies this limit.

Then output $n$ lines, each containing $m$ characters, describing the shape. If a cell in the rectangle is empty, output .; if it is a white cell, output W; if it is a black cell, output B.

The shape obtained from this rectangle must be connected, contain exactly $w$ white cells and $b$ black cells, and be colored in a chessboard pattern (a white cell can only be adjacent to an empty cell or a black cell, and a black cell can only be adjacent to an empty cell or a white cell).

2 2

3 5
.....
BWBW.
.....

3 4

3 7
.......
BWBWBWB
.......

3 100

-1

Hint

Scoring

A solution that works correctly for the case $w = b$ will receive at least $30$ points.

A solution that works correctly for the case $\max(w, b) \le 2 \cdot \min(w, b)$ will receive at least $60$ points.

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