A Knight's Journey#3454
The knight is getting bored of seeing the same black and white squares again and again and has decided to make a journey around the world. Whenever a knight moves, it is two squares in one direction and one square perpendicular to this. The world of a knight is the chessboard he is living on. Our knight lives on a chessboard that has a smaller area than a regular 8\times8 board, but it is still rectangular. Can you help this adventurous knight to make travel plans?
Find a path such that the knight visits every square once. The knight can start and end on any square of the board.
The input begins with a positive integer in the first line. The following lines contain test cases. Each test case consists of a single line with two positive integers and , such that 1 \leq p \times q \leq 26. This represents a p\times q chessboard, where describes how many different square numbers 1, \ldots, p exist, describes how many different square letters exist. These are the first letters of the Latin alphabet: A, \ldots, Z.
The output for every scenario begins with a line containing "Scenario #i:", where is the number of the scenario starting at . Then print a single line containing the lexicographically first path that visits all squares of the chessboard with knight moves, followed by an empty line. The path should be given on a single line by concatenating the names of the visited squares. Each square name consists of a capital letter followed by a number.
If no such path exists, you should output "impossible" on a single line.
Example 1