往届 ACM 队训练题 (参考)

1035. A Knight's Journey

单点时限: 2.0 sec

内存限制: 256 MB

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 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.

输入格式

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 . This represents a chessboard, where describes how many different square numbers exist, describes how many different square letters exist. These are the first letters of the Latin alphabet:

输出格式

The output for every scenario begins with a line containing Scenario #i:, where i 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 exist, you should output impossible on a single line.

样例

Input
3
1 1
2 3
4 3
Output
Scenario #1:
A1

Scenario #2:
impossible

Scenario #3:
A1B3C1A2B4C2A3B1C3A4B2C4
不限期开放

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