Problem D
Efficiency
Steve enjoys parties and word games. At one party, he
challenges his friends to play a new word game that he
invented.
In Steve’s game, there are four words: “Efficiency”, “Unbreaking”, “Silk”,
and “Touch”.
There are $P$ players
playing the game. At a given $N^{th}$ round, the players go
around in circles, each saying the word “Efficiency” once per
person, until the word has been said $N$ times. Then, starting with the
next player (right after the last player to say
“Efficiency”), they go around in the same fashion, each
saying “Unbreaking” until it has been said $N$ times. Lastly, continuing with
the next player, they go around saying “Silk” and “Touch”
alternately until both words have been said $N$ times.
For instance, in a game of $3$ people, the sequence of words is as follows:
|
$1^{st}$ Player |
$2^{nd}$ Player |
$3^{rd}$ Player |
|
Efficiency |
Unbreaking |
Silk (back to the $1^{st}$ player) |
|
Touch |
Efficiency |
Efficiency |
|
Unbreaking |
Unbreaking |
Silk |
|
Touch |
Silk |
Touch |
|
Efficiency |
Efficiency |
Efficiency |
|
Unbreaking |
Unbreaking |
Unbreaking |
|
Silk |
Touch |
Silk |
|
Touch |
Silk |
Touch (end of $3^{rd}$ round) |
Here, one can see that it takes $24$ turns (number of words said) to
complete three rounds of the game. Moreover, Player
$3$ goes last during the
third round.
Steve checks in at the $M^{th}$ turn, telling his friends to wrap up the game and go for a walk in the soul sand valley. Which word is being said at the $M^{th}$ turn, and who will go last in this round?
Input
The first line contains one integer $P$ ($1
\leq P \leq 1\, 000$), the number of players in the
game.
The second line contains one integer $M$ ($1
\leq M \leq 10^6$), which refers to the $M^{th}$ word that is said during the
game.
Output
The output should consist of two lines. On the first line, output the $M^{th}$ word said during the game; it should be one of “Efficiency”, “Unbreaking”, “Silk”, or “Touch”. On the second line, output an integer representing the player who goes last during this round (players are numbered $1, 2, 3, \ldots $).
| Sample Input 1 | Sample Output 1 |
|---|---|
3 24 |
Touch 3 |
| Sample Input 2 | Sample Output 2 |
|---|---|
1 19 |
Silk 1 |
