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문제

This is an interactive problem.

The lowest unique positive integer game is often used as an example of a game with very simple rules that is quite tricky for the computers to master.

$n$ players are playing this game, and it consists of $m$ rounds. In each round, each player chooses a positive integer in secret. The chosen integers are then revealed at the same time, and the player which has the lowest integer that was not chosen by any other player wins the round. In case all integers are repeated, there is no winner in that round.

In this problem you control $k$ players, $k>\frac{n}{2}$ (strictly more than half of all players), and your goal is for one of your players (not necessarily the same one) to win at least 90% of the rounds.

The other $n-k$ players will each play using a predetermined strategy that does not depend on your moves.

프로토콜

First, your program needs to read three integers $n$, $k$ and $m$ ($3 \le n \le 10$, $\frac{n}{2} < k < n$, $m$ is either 2 or 1000, and $m$ is 1000 in all cases except the sample case.

Then you need to repeat the following process $m$ times: you need to print $k$ integers between 1 and 100, inclusive, denoting the moves of the players you control. Remember to flush the output after doing that. Then you need to read $n-k$ integers, which will also be between 1 and 100, inclusive, denoting the moves of the remaining players in the round.

Your program must exit gracefully after completing $m$ rounds.

Your solution must win at least $0.9\cdot m$ rounds, rounded up.

예제 입력 1

5 3 2

1 1

2 3

예제 출력 1


2 3 3

100 50 1

노트

In the sample case, the other players will always choose 1 and 1 in the first round, and 2 and 3 in the second round.

There are 100 non-sample test cases in this problem.

채점

  • 예제는 채점하지 않는다.