Island Treasures

You are given an island exploration problem where Bob starts at an initial coordinate \((x_0, y_0)\) and must perform a specified sequence of movements repeatedly. Each test case provides:

• Initial conditions: the number of treasures \(n\), the number of repetitions \(M\) of the movement sequence, and Bob’s starting coordinates \((x_0, y_0)\).
• A list of \(n\) treasure coordinates \((a_i, b_i)\).
• A movement sequence that may include the following operations:
  • Translation (T dx dy): \((x, y) \to (x + dx, y + dy)\).
  • Vertical Scaling (VS sy): \((x, y) \to (x, y \times sy)\).
  • Horizontal Scaling (HS sx): \((x, y) \to (x \times sx, y)\).
  • Flip over x-axis (FX): \((x, y) \to (x, -y)\).
  • Flip over y-axis (FY): \((x, y) \to (-x, y)\).

Bob applies the entire movement sequence exactly \(M\) times. After these moves, for each treasure provided, if Bob's final coordinates exactly match a treasure's coordinates, output TREASURE FOUND; otherwise, output TREASURE LOST for that treasure. Each treasure’s result is printed on a new line.

inputFormat

The input is read from standard input (stdin) and has the following format:

P
n M x0 y0
a1 b1 a2 b2 ... an bn
K
[operation1]
[operation2]
...
[operationK]
... (repeated for each of the P test cases)

Where:

• P is the number of test cases.
• For each test case, the first line contains four integers: \(n\) (the number of treasures), \(M\) (the number of times the movement sequence is executed), \(x_0\), and \(y_0\) (the starting coordinates).
• The next line contains \(2n\) integers representing the coordinates of the treasures.
• The following line contains an integer K that denotes the number of moves in the sequence.
• Each of the next K lines describes a move in one of the following formats:
  • T dx dy for a translation.
  • VS sy for vertical scaling.
  • HS sx for horizontal scaling.
  • FX for flipping over the x-axis.
  • FY for flipping over the y-axis.

outputFormat

For each treasure in each test case, output a line with either TREASURE FOUND if Bob's final position matches the treasure's coordinates or TREASURE LOST otherwise. The output should be written to standard output (stdout).

## sample

3
2 1 0 0
2 3 -4 5
3
T 1 -1
VS 2
HS -1
1 1 0 0
1 -2
3
T 1 -1
VS 2
HS 1
2 2 0 0
2 3 -4 5
3
T 1 2
VS 1
HS 1

TREASURE LOST
TREASURE LOST
TREASURE FOUND
TREASURE LOST
TREASURE LOST

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