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No.8 Don't Say N Game

レベル : / AI推定難易度 : 675 / 実行時間制限 : 1ケース 5.000秒 / メモリ制限 : 512 MB / 標準ジャッジ問題
タグ : (AC するまで非表示) / 解いたユーザー数 790
作問者 : yuki2006
お気に入りにしたユーザー ProblemId : 26 / 自分の提出
問題文最終更新日: 2022-12-06 19:53:52
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Problem Statement

You and Grant are playing the so-called "Don't Say 21 Game" (also known in some places as a stick-taking game).

You go first, but no matter how many times you play this game you keep losing, so you extend the rules:

Using natural numbers \(N\) and \(K\), consider the following game.

1. First, the first player is given \(0\).
2. From there, the player declares the given number plus one of \( [1,K] (1~K) \), trying not to declare a number that is \(N\) or greater (declaring such a number loses the game), and passes it to the opponent.
3. The players take turns repeating step 2. until the game is decided.

You start the game as the first player.
Assuming that both players move so as not to lose, given natural numbers \(N,K\),
return \(Win\) if you can win, and \(Lose\) otherwise.

Here, you will play the game \(P\) times, changing \(N,K\) each time.
Determine the result of each game.

(This is easy for those who know something along these lines, but those who don't may need some difficult reasoning.)

Input

\(P\)
\(N_1\ K_1\)
\(N_2\ K_2\)
\(\dots\)
\(N_P\ K_P\)

On line \(1\), an integer \(P\ (1 \leq P \leq 100) \) representing the number of games is given.
Each of the following \(P\) lines contains integers \(N\ (2 \leq N \leq 120000) \) and \(K\ (2 \leq K \leq 120000) \) representing the conditions of a game.

Output

Output P lines in total, with the result of each game as Win or Lose.
Print a newline at the end of each line.

Sample

Sample 1
Input
1
21 3
Output
Lose

This is the ordinary "Don't Say 21 Game".
If the second player chooses numbers well,
the first player always loses.

Sample 2
Input
1
12 5
Output
Win

If the first player chooses numbers well,
the first player can win.

Sample 3
Input
3
5 10
40 6
100 8
Output
Win
Win
Lose

\(3\) games are played with different conditions.
Note that \(N \leq K\) is also possible.

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