Cards

Dave and Hal play a game with cards. Dave has $N$ cards, where $N$ is a multiple of three ($N = 3K$), and the cards are numbered from $1$ to $N$.

The same number is printed on both sides of a card, no two cards share a number, and the cards start sorted in increasing order.

First, Hal secretly picks one number from the set $\{1, 2, \ldots, N\}$.

Then Dave deals all the cards face up into a grid of $K$ rows and $3$ columns. He fills the grid row by row: card $1$, then card $2$, then card $3$ go into the first row from left to right, the next three cards fill the second row, and so on until the last card completes the last row.

Hal then tells Dave which column (the first, second, or third) currently holds the card with his secret number.

Dave gathers the cards column by column: he collects the entire first column from top to bottom (row $1$, row $2$, ..., row $K$), then the second column the same way, and finally the third column. Without shuffling, he deals this pile back onto the table exactly as before, row by row.

This repeats. Every time Dave finishes dealing, Hal again names the column that contains his card. After all of Hal's answers, several numbers may still be consistent with everything he said.

Write a program that uses Hal's answers to determine the smallest set of numbers that are still candidates for Hal's secret number.

The first line contains an integer $N$ ($3 \le N \le 999$, and $N$ is divisible by $3$), the number of cards.

The second line contains an integer $D$ ($1 \le D \le 10$), the number of deals, that is, the number of Hal's answers.

Each of the next $D$ lines contains one of the words first, second, or third - Hal's answer for that deal, given in order.

Print, on a single line, every number that is still a candidate for Hal's secret number, in increasing order, separated by single spaces.