404503: GYM101521 G Monorail

Monorail is a game featured in the Korean game show "The Genius". The main objective of Monorail is to form a loop using straight and curved track tiles. Here, we present a modified version of the game.

Percy is the only player and is given N straight tile and M curved track tiles. To win the game, he must place ALL of his tiles in a grid not larger than 100 × 100. Together, the tracks must be connected to form one single loop.

For example, a possible solution for N = 2 and M = 8 is shown below:

Help Percy determine if a solution exists, and if so, propose a valid solution.

The only line consists of two integers N and M, the number of straight track tiles and curved track tiles respectively.

For all input, 0 ≤ N, M ≤ 100 and N + M > 0.

If there is no solution, output Impossible.

Otherwise, output any valid solution. The first line should contain two integers, H and W, separated by a space. You are free to choose 1 ≤ H ≤ 100 and 1 ≤ W ≤ 100 as long as the grid is large enough for your solution. It is guaranteed that if there is a solution, then there exists a solution that fits in a 100 × 100 grid.

Then output the solution grid of height H and width W, consisting of the following characters:

• .: Empty cell
• -: Straight track tile (Figure 1a)
• |: Straight track tile (Figure 1b)
• 7: Curved track tile (Figure 2a)
• J: Curved track tile (Figure 2b)
• L: Curved track tile (Figure 2c)
• r: Curved track tile (Figure 2d)

Note: J, L and r are case-sensitive.

2 8

3 4
r-7.
L7L7
.L-J

0 4

4 4
....
.r7.
.LJ.
....

6 2

Impossible