Knight’s Journey

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

Background
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 reg-
ular 8 × 8 board, but it is still rectangular. Can you help this
adventurous knight to make travel plans?
The eight possible moves of a knight
Problem
Find a path such that the knight visits every square once. The knight can start and end on any square of the
board.

 

Input

The input begins with a positive integer n in the first line. The following lines contain n test cases.
Each test case consists of a single line with two positive integers p and q, such that 1 ≤ p · q ≤ 26.
This represents a p × q chessboard, where p describes how many different square numbers 1, . . . , p exist, q
describes how many different square letters exist. These are the first q letters of the Latin alphabet: A, . . .
 

Output

 The output for every scenario begins with a line containing "Scenario #i:", where i is the number
of the scenario starting at 1. 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 exist, you should output impossible on a single line.
 

Sample Input

3
1 1
2 3
4 3

Sample Output

Scenario #1:
A1
Scenario #2:
impossible
Scenario #3:
A1B3C1A2B4C2A3B1C3A4B2C4

Hint

 

Source

TU-Darmstadt Programming Contest 2005