**113 人解决**，162 人已尝试。

**200 份提交通过**，共有 638 份提交。

**3.6** EMB 奖励。

**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.

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:

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.

Input

3 1 1 2 3 4 3

Output

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

**113 人解决**，162 人已尝试。

**200 份提交通过**，共有 638 份提交。

**3.6** EMB 奖励。

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