- Prepare
- Algorithms
- Game Theory
- A Chessboard Game

# A Chessboard Game

# A Chessboard Game

Two players are playing a game on a chessboard. The rules of the game are as follows:

The game starts with a single coin located at some coordinates. The coordinates of the upper left cell are , and of the lower right cell are .

In each move, a player must move the coin from cell to one of the following locations:

**Note:**The coin must remain inside the confines of the board.Beginning with player 1, the players alternate turns. The first player who is unable to make a move loses the game.

The figure below shows all four possible moves using an board for illustration:

Given the initial coordinates of the players' coins, assuming optimal play, determine which player will win the game.

**Function Description**

Complete the *chessboardGame* function in the editor below. It should return a string, either `First`

or `Second`

.

chessboardGame has the following parameter(s):

*x*: an integer that represents the starting column position*y*: an integer that represents the starting row position

**Input Format**

The first line contains an integer , the number of test cases.

Each of the next lines contains space-separated integers and .

**Constraints**

**Output Format**

On a new line for each test case, print if the first player is the winner. Otherwise, print .

**Sample Input**

```
3
5 2
5 3
8 8
```

**Sample Output**

```
Second
First
First
```

**Explanation**

In the first case, player1 starts at the red square and can move to any of the blue squares. Regardless of which one is chosen, the player 2 can move to one of the green squares to win the game.

In the second case, player 1 starts at the red square and can move to any of the blue squares or the purple one. Moving to the purple one limits player 2 to the yellow square. From the yellow square, player 1 moves to the green square and wins.