meetforever/GRPO_CL huggingface dataset:
user: A long time ago in a galaxy far, far away, there were $N$ planets. There were also $N - 1$ interplanetary paths that connected all the planets (directly or indirectly). In other words, the network of planets and paths formed a tree. Additionally, each path was enumerated with an integer that denoted the curiosity of the path.

A pair of planets $A$, $B$ is boring if the following holds:
 - $A$ and $B$ are different planets;
 - travelling between planet $A$ and $B$ is possible using one or more interplanetary paths; and
 - the binary XOR of the curiosity of all the paths in that travel is equal to 0

Alas, the times have changed and an evil emperor is ruling the galaxy. He decided to use the Force to destroy all the interplanetary paths in a certain order. Determine the number of boring pairs of planets before the emperor started the destruction and after each destruction.

-----Input-----
The first line of input contains the integer $N$ ($1 \leq N \leq 100000$). Each of the following $N - 1$ lines contains three integers $A_ i$, $B_ i$, $Z_ i$ ($1 \leq A_ i, B_ i \leq N$, $0 \leq Z_ i \leq 1000000000$) that denote that planets $A_ i$ and $B_ i$ are directly connected with a path of curiosity $Z_ i$. The following line of input contains the permutation of the first $N - 1$ integers that denote the order in which the emperor is destroying the paths. If the $i$-th element of the permutation is $j$, then the emperor destroyed the path between planets $A_ j$ and $B_ j$ in the $i$-th step.

-----Output-----
The output must contain $N$ lines, the $k$-th line containing the number of boring pairs A, $B$ from the task after the emperor destroyed exactly $k - 1$ paths.

-----Examples-----
Sample Input 1:
2
1 2 0
1
Sample Output 1:
1
0

Sample Input 2:
3
1 2 4
2 3 4
1 2
Sample Output 2:
1
0
0
user: One day you and GTmac walk into a classroom and see a mysterious expression on the blackboard:\[ (1^b + 2^b + \cdots + a^b)~ \mathrm{mod}~ a \]

Upon seeing the expression GTmac shows an evil smile and challenges you: “Let me give you the values of $a$ and $b$ and let’s assume $b$ is an odd number. Want to bet who can evaluate this expression? The one who loses shall buy pizza for us tonight.”

-----Input-----
The input has two integers $a$ ($1 \leq a \leq 10^9$) and $b$ ($1\leq b\leq 99$, $b$ is odd) on a single line.

-----Output-----
Output the value of the expression with the given $a$ and $b$.

-----Examples-----
Sample Input 1:
2 3
Sample Output 1:
1

Sample Input 2:
3 7
Sample Output 2:
0
user: Ruben and Albert are what you can call abnormally smart. They are also both very fond of mathematically inspired games. Their only problem is that most games are too easy for them, and they end up beating everyone who dares challenge them. Because of that, they’re now mostly playing against each other. To make things interesting, they had a professor design a new game for them.

This new game was interesting at first. Nowadays, however, Albert often complains that it is impossible for him to win a particular round. After long discussions, they’ve now decided to take this a step further, and actually figure out who’d win if they both played optimally. They need you to write a computer program that does this for them.

A state in the game consists of one or more $x\times y\times z$ cuboids. A (legal) move is choosing a cuboid, then a value for each of the three axes (basically choosing three planes), and then cutting the cuboid along these (thus removing a $1\times y\times z$, $x\times 1\times z$ and a $x\times y\times 1$, all overlapping, cuboid). In effect you’ve created between $0$ and $8$ (inclusive) smaller cuboids. All three planes cut from the cuboid need to be on the cuboid (you can’t cut away a hypothetical cuboid on the outside of the real one).

An example might be in order. You’ve chosen a $3\times 5\times 4$ cuboid, and are about to cut it. You now need to choose the three planes. This means you need an $x$ between $1$ and $3$, a $y$ between $1$ and $5$ and a $z$ between $1$ and $4$. Say you choose $2$, $1$ and $3$, respectively. The first cut would alone cut the cuboid into two $1\times 5\times 4$ cuboids, the second into a single $3\times 4\times 4$ cuboid, while the third would alone cut the cuboid into a $3\times 5\times 1$ and a $3\times 5\times 2$ cuboid. Put together these cuts produces $4$ new smaller cuboids, of sizes $1\times 4\times 1$,$1\times 4\times 1$,$1\times 4\times 2$ and $1\times 4\times 2$. Note that cutting a cuboid with an axis of size $1$ would remove it altogether.

The players take turns making a move. The winner is the player that removes the last cuboid.

-----Input-----
The first line of input is a line containing either RUBEN or ALBERT, the name of the player who starts that particular round.

 Then follows a line containing $N$, the number of cuboids that particular game starts with.

$N$ lines follow, each describing a cuboid. A cuboid description consists of three numbers, $x$, $y$ and $z$, the size of that particular cuboid.

-----Output-----
Output the name of the player that wins the game (either RUBEN or ALBERT).

-----Limits-----
 - $1 \le N \le 100$
 - $1 \le x,y,z \le 30$

-----Examples-----
Sample Input 1:
RUBEN
1
4 1 7
Sample Output 1:
RUBEN

Sample Input 2:
ALBERT
2
4 4 4
2 2 2
Sample Output 2:
RUBEN
user: First Orchard is a cooperative game for children 2 years and up. In this simple game, the players pick colored fruits from trees in an orchard and place them into a basket. To make the game more interesting, a raven tries to reach the orchard to steal the fruits. If the players are successful in moving all fruits into the basket before the raven can get to the orchard, they’ll win. If the raven gets there first, the players lose!

Your task is to determine the probability with which the players will win!

The game is played as follows. There are $4$ trees in the orchard, each bearing a different type of fruit: red apples, green apples, blue plums, and yellow pears. The raven tries to reach the orchard through a pathway containing one or more steps.

At each turn, the players roll a six-sided die. Four of the faces show a color (red, green, yellow, blue), the fifth face shows a fruit basket, and the sixth face shows a raven. All six faces can appear with equal probability.
 - Red, Green, Yellow, Blue. In these cases, a fruit with the corresponding color is placed into the basket, provided the tree corresponding to this color still has any fruits left to pick. Otherwise, the players move on to the next turn.
 - Fruit Basket. If the players roll the ’basket’ face, they will pick a fruit from the tree that has the largest number of fruits left. If there are multiple such trees with the same number of fruits, any of the trees can be chosen.
 - Raven. If the ’raven’ face appears on the die, then the raven moves one step closer towards the orchard.

The game is over if either the players have picked all fruits, or if the raven reaches the orchard, whichever happens first. If the raven reaches the orchard before the players have placed all fruits into the basket, the players lose.

-----Input-----
The input consists of a single test case with a single line of input. The input contains five integer numbers: $R$, $G$, $B$, $Y$ and $S$. The values of $R, G, B$ and $Y$ are the number of red, green, blue, and yellow fruits initially on each tree, respectively, and $S$ denotes the number of steps on the raven’s pathway. Since the game is intended for young children, there will be at most $4$ fruits of each color: $0 \le R, G, B, Y \le 4$. There will be at least one fruit overall: $0 < R + G + B + Y$. The raven will require at least $1$ and at most $8$ steps: $1 \le S \le 8$. The number of steps is equal to the number of times the raven must appear on the die for the players to lose.

-----Output-----
Output the probability that the players will win as a floating point number. The absolute error of your result should be less than $10^{-5}$.

-----Examples-----
Sample Input 1:
1 1 0 0 3
Sample Output 1:
0.920138888889

Sample Input 2:
4 4 4 4 5
Sample Output 2:
0.631357306601
user: Alice and Bob created a new game while at the beach this summer. All they need is a set of numbered playing cards. They start by creating $P$ piles with all cards face-up and select a non-negative number $K$. After that, they take turns like this:
 - A player starts by selecting one of the piles.
 - Then, he removes from $0$ up to $K$ cards from the top of that pile, leaving at least one card in the pile.
 - Next, he looks at the card left at the top of the pile and must remove a number of cards equal to its value (from the top of the same pile).

Whoever doesn’t have more cards to remove, or whoever is forced to remove more cards than those available on a pile, loses the game.In the figure, you can see an example with two piles and $K = 1$. The player to move might: 
 - Select the first pile and $0$ cards to remove, being forced to remove $1$ card from the top next.
 - Select the second pile and $0$ cards to remove, having to remove $1$ card from the top next.
 - Select the second pile and $1$ card to remove, having to remove $2$ cards from the top next.

Alice has realized that Bob is very good at this game and will always win if he has the chance. Luckily, this time Alice is first to play. Is Alice able to win this game?

-----Task-----
Given the description of the piles with all the cards and the maximum number of cards they can start to remove, your goal is to find out whether Alice can win the game if she is the first to play.

-----Input-----
The first line contains $2$ space separated integers, $P$, the number of piles, and $K$, the maximum number of cards they can start to remove on their turn. The next $P$ lines start with an integer $N$, indicating the number of cards on a pile. $N$ space separated integers follow, representing the cards on that pile from the bottom to the top.

-----Constraints-----

$1 \leq P \leq 100$

Number of piles.

$1 \leq K \leq 10$

Maximum number of cards a player can start to remove.

$1 \leq c \leq 10$

Number on each card.

$1 \leq N \leq 1000$

Size of each pile.

-----Output-----
A single string, stating “Alice can win.” or “Bob will win.”, as appropriate.

-----Sample Output Explanation-----
In the first sample, the piles are the same, so Bob will always be able to mirror whatever move Alice makes.

In the second sample, Alice can start by removing $0$ cards from the second pile and then $1$ card from its top. Two legal moves will be possible next, Bob will make one and Alice the other.

-----Examples-----
Sample Input 1:
4 1
4 1 1 1 1
6 2 1 2 1 2 1
4 1 1 1 1
6 2 1 2 1 2 1
Sample Output 1:
Bob will win.

Sample Input 2:
2 1
1 1
3 1 2 1
Sample Output 2:
Alice can win.
user: Margriet A. is in pizza heaven! She has bought a one-day access pass to Pizza World. Pizza World is a food festival, where all stands have their own special type of pizza. Margriet would really like to try many different types of pizza, but she thinks that she can only eat two pizzas in total. Therefore, she has come up with a cunning plan: at each stall she visits she decides whether she wants to buy this pizza or not. At the first stall where she decides to make a purchase, she buys and eats exactly one pizza. At the second one, she buys and eats half a pizza, and at the third she eats one quarter of a pizza, etc. …Therefore, at the $k^\textrm {th}$ stall where she decides to buy some pizza, she eats $\frac1{2^{k-1}}^\textrm {th}$ part of a pizza. This way she makes sure that she never gets full!

In order to ensure that the flow of people in the park is adequate, the pizza stalls are connected by one-way paths, and to make sure that everyone eventually leaves the festival, it is impossible to visit a pizza stall more than once. However, every stall is reachable from the stall at the entrance, which is the stall with number $0$.

Of course, Margriet has her own taste: she likes some pizzas more than others. Eating pizza from a stall gives her a certain amount of satisfaction which is equal to Margriet’s personal stall satisfaction number multiplied by the fraction of a whole pizza she eats there. Her total satisfaction is the sum of satisfactions of every stall she visits. Can you help Margriet plot a route between the pizza stalls that satisfies her the most?

-----Input-----
 - The first line has two integers, $1\leq n \leq 5 \cdot 10^5$ and $0\leq m \leq 5 \cdot 10^5$, the number of pizza stalls and the number of one way connections.
 - The second line has $n$ integers $c_0, \dots , c_{n-1}$, where each $0\leq c_ i \leq 10^9$, the amount of satisfaction Margriet gets from eating one pizza at stall $i$.
 - The next $m$ lines each contain $2$ integers, $0\leq s<n$ and $0\leq t<n$, indicating a one way path from stall $s$ to stall $t$. No connection appears twice in the input.

-----Output-----
 - Print the maximal amount of satisfaction Margriet can reach at the pizza festival. Your answer is considered correct if it has absolute or relative error of at most $10^{-6}$.

-----Examples-----
Sample Input 1:
5 5
1 4 6 2 100
0 1
1 2
0 3
2 4
3 4
Sample Output 1:
100

Sample Input 2:
3 2
1 0 1
0 1
1 2
Sample Output 2:
1.5
user: Your friend Claire has dragged you along to a speedcubing event that is happening in Eindhoven. These events are all about solving the Rubik’s cube and similar twisty puzzles as quickly as possible. The attendants of the event can enter into various competitions based on the type and size of the puzzle, and there are even special competitions where the puzzles need to be solved one-handed or blindfolded. 

Claire is competing in the most popular competition: speedsolving the $3\times 3\times 3$ Rubik’s cube, pictured on the right. Each contestant needs to solve the cube five times, each time with a different random scramble. After all solves are completed, the best and the worst times are discarded and the final score is the average of the remaining three times. The contestant with the smallest final score wins.

Claire has done well in the competition so far and is among the contenders for the overall victory. All the other contestants have already finished their five solves, but Claire has one solve remaining. By looking at the final scores of the other contestants, she has deduced her own target final score. As long as her final score is less than or equal to this target score, she will be declared the overall winner. Is it possible for her to win the competition, and if so, what is the worst time she can have on her last solve in order to do so?

-----Input-----
The input consists of:
 - One line with four real numbers $t_1$, $t_2$, $t_3$ and $t_4$, the times Claire got on her first four solves.
 - One line with a real number $t$, Claire’s target final score, the worst final score she can have in order to be declared the overall winner.

Each number is between $1$ and $20$, inclusive, and is given with exactly two decimal places.

-----Output-----
If it is not possible for Claire to win the event, output “impossible”. If she will win regardless of the time she gets on her last solve, output “infinite”. Otherwise, output the worst time she can have on her last solve in order to be declared the overall winner. Output the number to exactly two decimal places.

-----Examples-----
Sample Input 1:
6.38 7.20 6.95 8.11
7.53
Sample Output 1:
infinite

Sample Input 2:
6.38 7.20 6.95 8.11
6.99
Sample Output 2:
6.82
user: You are playing a game in which a group of players take turns saying animal names. The animal name you say when it is your turn must start with the same letter as the previously said animal ends with and it must not have been said previously in this round of the game. If there is no valid name or you cannot come up with one you are eliminated. 

Given the last animal name said before your turn and a list of all names not yet used, can you make it through this turn? If so, can you make sure to eliminate the next player?

-----Input-----
The first line of input contains a single word, the animal that the previous player just said. The next line contains a single integer $n$ ($0 \le n \leq 10^5$), the number of valid unused animal names. Each of the following $n$ lines contains one valid unused animal name.

All animal names (including the one the previous player said) are unique and consist of at least $1$ and at most $20$ lower case letters ‘a’-‘z’.

-----Output-----
If there is any animal name you can play that eliminates the next player, output the first such name from the input list, followed by an exclamation mark. Otherwise, if there is any animal name that you can play, output the first such name. Otherwise, output a question mark (in this case you will just have to make up a fake name in the hope that the others will trust you that this is a real animal).

-----Examples-----
Sample Input 1:
pig
2
goat
toad
Sample Output 1:
goat

Sample Input 2:
dog
2
snake
emu
Sample Output 2:
?
user: The impending doom called final examination is approaching this year’s high school seniors: one of the compulsory tasks is going to be writing an essay in their mother tongue. Mirko is under the impression that certain political parties are going to keep their promises, those regarding informatization and digitalization, which is why he thinks that this year’s essays are going to be marked by a computer, instead of a human.

To test his doubts, Mirko is going to write an essay that doesn’t necessarily make sense at all, but should pass the automatic basic conditions check. The essay passes the check if
 - it contains at least $A$, and at most $B$ words;
 - every word contains at least one, and at most 15 letters;
 - the used vocabulary is large enough, in other words, the essay contains at least $B/2$ different words.

Mirko was up late last night watching Big Brother, so he is asking you to write such an essay instead of him. The essay should be output in a single line, using only lowercase letters of the English alphabet and spaces (therefore, without punctuation such as dots, commas and such). The words used can, but need not be, words from the English (or any) language.

-----Input-----
The first and only line of input contains the integers $A$ and $B$ ($1 \leq A \leq B \leq 100000$) from the task.

-----Output-----
The first and only line of output must contain any essay that meets the rules from the task.

-----Examples-----
Sample Input 1:
2 7
Sample Output 1:
dobar je ovaj marko marulic

Sample Input 2:
26 30
Sample Output 2:
nama je profesor reko da to ne treba za lektiru al onda je bila buka i nisam ga cuo pa jel bi mi mogli dat bodove
user: Little Frane is already in tenth grade, but is still struggling with Pascal in computer class. For homework, his teacher wrote the following program into his notebook, and he needs to determine the output, given the integer $N$.

readln(N);
counter := 0;
for i := N - 1 downto 1 do begin
  counter := counter + 1;
  if N mod i = 0 then break;
end;
writeln(counter);

Write a program which solves Frane’s problem.

-----Input-----
The first and only line of input contains the integer $1 \le N \le 10^9$.

-----Output-----
Output the result from Frane’s program on a single line.

-----Examples-----
Sample Input 1:
1
Sample Output 1:
0

Sample Input 2:
10
Sample Output 2:
5
user: The mole family recently decided to dig a new tunnel network. The layout, which has already been decided, consists of chambers and bidirectional tunnels connecting them, forming a connected graph. Mother mole wants to use the opportunity to teach her two mole kids how to dig a tunnel network. 

As an initial quick demonstration, mother mole is going to start by digging out a few of the chambers and tunnels, in the form of a non-self-intersecting path in the planned tunnel network. She will then divide the remaining chambers between the two mole kids, making sure that each mole kid has to dig out the same number of chambers, or else one of the mole kids will become sad. (The tunnels are much easier to dig out, and thus of no concern.) The kids may work on their assigned chambers in any order they like.

Since the mole kids do not have much experience with digging tunnel networks, mother mole realises one issue with her plan: if there is a tunnel between a pair of chambers that are assigned to different mole kids, there is a risk of an accident during the excavation of that tunnel if the other mole kid happens to be digging in the connecting chamber at the same time.

Help mother mole decide which path to use for her initial demonstration, and how to divide the remaining chambers evenly, so that no tunnel connects a pair of chambers assigned to different mole kids. The initial path must consist of at least one chamber and must not visit a chamber more than once.

-----Input-----
The input consists of:
 - One line with two integers $c$ and $t$ ($1 \leq c \leq 2 \cdot 10^5$, $0 \leq t \leq 2 \cdot 10^5$), the number of chambers and tunnels in the planned tunnel network.
 - $t$ lines, each containing two integers $a$ and $b$ ($1 \leq a,b \leq c$, $a \neq b$), describing a bidirectional tunnel between chambers $a$ and $b$.

The chambers are numbered from $1$ to $c$. There is at most one tunnel between any pair of chambers, and there exists a path in the network between any pair of chambers.

-----Output-----
First output two integers $p$ and $s$, the number of chambers on the path in mother mole’s initial demonstration and the number of chambers each mole kid has to dig out. Then output a line containing the $p$ chambers in mother mole’s initial path, in the order that she digs them out. Then output two more lines, each containing the $s$ chambers that the respective mole kid has to dig out, in any order.

The input is chosen such that there exists at least one valid solution. If there are multiple valid solutions, you may output any one of them.

-----Examples-----
Sample Input 1:
3 2
3 1
2 1
Sample Output 1:
3 0
3 1 2

Sample Input 2:
4 3
1 3
2 3
3 4
Sample Output 2:
2 1
3 4
2
1
user: Ms. Thomas is managing her class of $n$ students.

She placed all her students in a line, and gave the $i$-th student from the left a card with the letter $a_ i$ written on it.

She would now like to rearrange the students so that the $i$-th student from the left has a card with the letter $b_ i$ written on it.

To do this, she will choose some consecutive group of students, and reverse their order. Students will hold on to their original cards during this process.

She’s now wondering, what is the number of valid ways to do this? (It may be impossible, in which case, the answer is zero).

With sequences $abba$ and $aabb$, Ms. Thomas can choose the group $a(bba)$. With sequences $caxcab$ and $cacxab$, Ms. Thomas can choose $ca(xc)ab$ or $c(axca)b$. With sequences $a$ and $z$, there are clearly no solutions.

-----Input-----
The input is two lines of lowercase letters, $A$ and $B$. The $i$-th character of $A$ and $B$ represent $a_ i$ and $b_ i$ respectively. It is guaranteed that $A$ and $B$ have the same positive length, and $A$ and $B$ are not identical. The common length is allowed to be as large as $100000$.

-----Output-----
For each test case, output a single integer, the number of ways Ms. Thomas can reverse some consecutive group of $A$ to form the line specified by string $B$.

-----Examples-----
Sample Input 1:
abba
aabb
Sample Output 1:
1

Sample Input 2:
caxcab
cacxab
Sample Output 2:
2