Rock Paper Scissors Lizard Spock

Leo plays rock, paper, scissors, lizard, Spock against his computer. The game runs in rounds, and in every round the two players pick one of five options at the same time: rock, paper, scissors, lizard, Spock. Each option beats exactly two of the other four.

If both players pick the same option, the round is a draw.

Figure F.1: the mechanics of the game. Illustration by VidTheKid via Wikimedia Commons.

Leo's computer picks its option with a linear congruential generator. The generator uses a known prime $p = 127$ and two fixed integers $0 \le a < p$ and $0 \le b < p$ that Leo does not know. It also keeps a state $0 \le x < p$ whose starting value Leo does not know either. Before every round the computer updates the state,

$x \leftarrow (a \cdot x + b) \bmod p,$

and then reads its option out of this table.

Leo watched the first $n$ rounds and wrote down everything the computer played. He wants to win every one of the next $m$ rounds. Two options beat any given option, and Leo always takes the one that comes first in the order rock, paper, scissors, lizard, Spock.

Print what Leo plays in each of the next $m$ rounds.

The first line has two integers $n$ and $m$ ($1 \le n \le 1000$, $1 \le m \le 1000$).

Each of the next $n$ lines holds one of the words rock, paper, scissors, lizard, Spock: what the computer played in that round, in order.

The recorded rounds come from a generator of the form above, and they determine the next $m$ options. Every triple $(a, b, x)$ that reproduces all $n$ recorded options produces the same $m$ options after them.

Print $m$ lines. Line $i$ holds what Leo plays in round $n + i$: the option that beats the computer's choice in that round, and when two options beat it, the one that comes first in the order rock, paper, scissors, lizard, Spock.