The Stripe Game

The Stripe Game is a two‐player impartial game played on a 1D board (or strip) composed of p consecutive squares. There are three types of colored stripes available: red, green, and blue. Each stripe is a rectangular tile of size:

• Red stripe: \(c\times1\)
• Green stripe: \(z\times1\)
• Blue stripe: \(n\times1\)

Both players have an unlimited supply of each type of stripe. The board is a \(p\times1\) rectangle (i.e. it has \(p\) cells of size \(1\times1\)). Players take turns placing a stripe onto the board subject to the following rules:

1. The stripe must lie completely within the board.
2. The stripe cannot overlap any previously placed stripe (even partially).
3. The stripe must be aligned with the boundaries of the cells.

The first player who cannot make a move loses the game. The question is: does the first player always have a winning strategy regardless of how the opponent plays?

Your task is to write a program that:

1. Reads the three stripe sizes and at least one board size \(p\) (there can be several boards).
2. For each board, determines if the first player (the starting player) is guaranteed a win.
3. Outputs the results.</p>

   Game Theory Note: This is a combinatorial game that can be solved using the Sprague-Grundy theorem. For a board (or free segment) of length \(L\), let the Grundy value \(G(L)\) be defined as:

   \[ G(L) = \text{mex} \Big\{ G(i) \oplus G(L - r - i) \;\big|\; r \in \{c, z, n\}, \; 0 \le i \le L - r \Big\} \]

   If \(L < \min(c, z, n)\) then no move is possible and \(G(L)=0\). The first player has a winning strategy if and only if \(G(p)\neq0\).

   inputFormat

   The input begins with a single line containing three positive integers \(c\), \(z\), and \(n\), representing the stripe sizes (red, green, and blue respectively). The next line contains a positive integer \(T\) representing the number of board queries. Each of the following \(T\) lines contains a positive integer \(p\) representing the board length.

   Example:

   2 3 4
   3
   1
   5
   7
   

   outputFormat

   For each board query, output a single line with either Win if the first player has a winning strategy for that board or Lose otherwise.

   Example Output:

   Lose
   Win
   Win
   

   sample

   2 3 4
   3
   1
   5
   7
   

   Lose
   Win
   Win
   

   </p>