### A 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 regular 8 * 8 board, but it is still rectangular.

Can you help this adventurous knight to make travel plans?

Problem Find a path such that the knight visits every square once. The knight can start and end on any square of the board.

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 * 8 board, but it is still rectangular.

Can you help this adventurous knight to make travel plans?

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

poj2488 有链接提示的题目请先去链接处提交程序，AC后提交到SDUTOJ中，以便查询存档。

#### Source

深度优先搜索练习