meetforever/GRPO_CL huggingface dataset:
user: “Hey! I have an awesome task with chameleons, $5$-th task for Saturday’s competition.”

“Go ahead…”

(…)

“That’s too difficult, I have an easier one, they won’t even solve that one.”

“You are given an array of $N$ integers from the interval $[1, K]$. You need to process $M$ queries. The first type of query requires you to change a number in the array to a different value, and the second type of query requires you to determine the length of the shortest contiguous subarray of the current array that contains all numbers from $1$ to $K$.”

“Hm, I can do it in $\mathrm{O}(N^6)$. What’s the limit for $N$?”

-----Input-----
The first line of input contains the integers $N$, $K$ and $M$ ($1 \leq N, M \leq 100000$, $1 \leq K \leq 50$). The second line of input contains $N$ integers separated by space, the integers from the array. After that, $M$ queries follow, each in one of the following two forms:
 - “1 p v”—change the value of the $p$-th number into $v$ ($1 \leq p \leq N, 1 \leq v \leq K$)
 - “2”—what is the length of the shortest contiguous subarray of the array containing all the integers from $1$ to $K$.

-----Output-----
The output must consist of the answers to the queries of the second type, each in its own line. If the required subarray doesn’t exist, output -1.

-----Examples-----
Sample Input:
4 3 5
2 3 1 2
2
1 3 3
2
1 1 1
2
Sample Output:
3
-1
4
user: Your dog Spot is let loose in the park. Well, relatively loose – he is tied to a post with a leash, limiting his movements. Spread around the park are various squeaky toys and other dog paraphernalia, which Spot happily goes after when he sees them. When he gets to a toy he will chew at it for a while until it has become defunct, at which point he will go after the next toy, which looks much squeakier.

This is all very well, but there are obstacles to Spot’s joyful canine play: trees. In the park there are several trees, and if Spot walks around a tree his leash gets wrapped around the tree, making his movements more limited. Being a dog, with pressing squeaky matters to attend to, Spot does not really have time to take things such as trees into account, and always goes directly in a straight line for his next toy. If he can’t get to his next toy because he has run out of leash, Spot will start barking uncontrollably (as no doubt any of us would) and you have to help him. How long would Spot’s leash have to be in order for him to run out of toys before he runs out of leash?

For practical purposes, you may assume that (when seen from above) Spot, his toys, and the trees are points, and that the post that the leash is tied to will not hinder Spot’s movements in any way. After having finished chewing a toy, Spot always goes for the most shiny unchewed toy. The post to which Spot’s leash is tied is located at coordinates $(0,0)$, and this is also where Spot is initially located.

-----Input-----
The first line of input consists of two integers $n$ and $m$, where $1 \le n \le 50$ is the number of toys in the park and $0 \le m \le 50$ is the number of trees in the park. Then follow $n$ lines, each containing two integers $x$, $y$ giving the coordinates of a toy. The toys are listed in decreasing order of shininess. This is followed by $m$ lines, each containing two integers $x$, $y$, indicating that there is a tree at those coordinates.

Each coordinate is bounded by 10000 in absolute value. The toys, the trees and the post are all in different positions, and Spot’s route will never take him within distance 0.001 of any tree.

-----Output-----
Write a single line containing the length needed for the leash in order for Spot to be able to get to all his toys, rounded to two decimal digits.

-----Examples-----
Sample Input:
2 0
10 0
10 10
Sample Output:
14.14
user: Several surveys indicate that the taller you are, the higher you can climb the corporate ladder. At TALL Enterprises Inc., this “de facto standard” has been properly formalized: your boss is always at least as tall as you are. Furthermore, you can safely assume that your boss earns a bit more than you do. In fact, you can be absolutely sure that your immediate boss is the person who earns the least among all the employees that earn more than you and are at least as tall as you are. Furthermore, if you are the immediate boss of someone, that person is your subordinate, and all of his or her subordinates are your subordinates as well. If you are nobody’s boss, then you have no subordinates. As simple as these rules are, many people working for TALL are unsure of to whom they should be turning in their weekly progress report and how many subordinates they have. Write a program that will help in determining for any employee who the immediate boss of that employee is and how many subordinates they have. Quality Assurance at TALL have devised a series of tests to ensure that your program is correct. These test are described below.

-----Input-----
On the first line of input are two positive integers $m$ and $q$, where $m$ (at most $100000$) is the number of employees and $q$ (at most $10000$) is the number of queries. The following $m$ lines each list an employee by three integers on the same line: employee ID number (six decimal digits, the first one of which is not zero), yearly salary in Euros and finally height in $\mu $m ($1 \mu \text {m} = 10^{-6}$ meters – accuracy is important at TALL). The chairperson is the employee that earns more than anyone else and is also the tallest person in the company. Then there are $q$ lines listing queries. Each query is a single legal employee ID.

The salary is a positive integer which is at most $10000000$. No two employees have the same ID, and no two employees have the same salary. The height of an employee is at least $1000000$ $\mu $m and at most $2500000$ $\mu $m.

-----Output-----
For each employee ID $x$ in a query output a single line with two integers $y$ and $k$, where $y$ is the ID of $x$’s boss, and $k$ is the number of subordinates of $x$. If the query is the ID of the chairperson, then you should output $0$ as the ID of his or her boss (since the chairperson has no immediate boss except, possibly, God).

-----Examples-----
Sample Input:
3 3
123456 14323 1700000
123458 41412 1900000
123457 15221 1800000
123456
123458
123457
Sample Output:
123457 0
0 2
123458 1
user: In the dangerous wild west, robbers are attacking a long train with many coaches. Chaos erupts, and the robbers realize that the amount of chaos equals the number of passengers in the train, rounded up to the nearest multiple of $10$. In order to quench the chaos, they therefore decide to kill some passengers by blowing up one of the coaches.

What the robbers failed to realize, however, is that when there are multiple disjoint train segments, then the total amount of chaos is equal to the sum of the chaos of each train segment times the number of train segments!

Frantic to quench the now even worse chaos, the robbers continue blowing up every coach until all passengers are dead. Phew!

The chaos in a train segment is equal to the number passengers in that train segment rounded up to the nearest multiple of $10$. What was the maximum amount of chaos during the robbery?

-----Input-----
On the first line is a single integer $n$, ($3 \leq n \leq 100000$), the number of coaches in the train. On the second line follows $n$ integers $p_1, p_2, \ldots p_ n$, ($0 \leq p_ i \leq 100$ for each $i \in \{ 1, 2, \ldots , n\} $) the number of passengers in each coach. On the third and final line follows a permutation of the numbers from $1$ to $n$ indicating the order in which the robbers blew up the coaches.

-----Output-----
A single integer, the maximum chaos that occurred during the robbery.

-----Examples-----
Sample Input:
5
3 5 10 2 5
2 4 5 1 3
Sample Output:
90
user: The mayor has decided that it is high time to implement a new system of television transmitters. The city can be represented as a segment of the length $D$ on which there are buildings of different heights. The width of a building is negligible. On top of some buildings, television transmitters are set, their dimensions are also negligible.

Television transmitters emit a television signal in all directions around them. The signal is spread through space in straight lines and cannot pass through buildings. A certain point in the city is considered covered if it is reached by a signal from an existing transmitter.


Find the segment of the city covered by television signal and output its length.

-----Input-----
The first line of input contains the integer $N$ ($1 \leq N \leq 3 \cdot 10^5$), the number of buildings, and the integer $D$ ($1 \leq D \leq 10^9$), the city length.

Each of the following N lines contains three numbers which describe the $i$-th building:
 - a number which determines whether there is a transmitter on top of the building: 0 (no) or 1 (yes)
 - an integer $X_ i$ ($0 \leq X_ i \leq D$), the distance between the building and the left end of the city
 - an integer $H_ i$ ($1 \leq H_ i \leq 10^9$), the building height

The buildings are sorted in ascending order by the distance from the left end of the city. No two buildings will be located on the same distance from the left end of the city.

-----Output-----
The first and only line of output must contain the required length from the text. Note: the maximum permissible deviation from the official solution is 10-3 in absolute value.

-----Examples-----
Sample Input:
3 10
1 2 6
0 4 3
0 8 2
Sample Output:
6.000000
user: Nowadays, there are a lot of unusual people. We won’t go into details, but instead focus on a certain type, to us personally the most interesting people. Of course, we’re talking about barbarians!

There are a lot of barbarians, but only a few of them are truly important. This story has $N$ important barbarians, denoted with integers from $1$ to $N$. Each of them has their own stone tablet with their word written on it, consisting of only lowercase letters of the English alphabet.

Our barbarians are playing an interesting game with their good friend Tarzan.

The game is played in $Q$ rounds. There are two round types and each is determined by Tarzan:1st type:

Tarzan shows the word $P$ to the barbarians.2nd type:

Tarzan asks the barbarian denoted with $S$ the following question: “Out of all the words I’ve shown you so far, how many of them have the word on your stone tablet as a consecutive substring?”

Given the fact that the barbarians go wild a lot and aren’t really able to pay attention and keep up with what’s happening in the game, they need your help. Help the barbarians answer each of Tarzan’s questions correctly.

-----Input-----
The first line of input contains the integer $N$ ($1 \leq N \leq 10^5$), the number of barbarians.

Each of the following $N$ lines contains a single word consisting of only lowercase letters of the English alphabet, the $i$-th word corresponding to the word on the stone tablet of barbarian denoted with $i$.

After that, the integer $Q$ ($1 \leq Q \leq 10^5$) follows, the number of rounds in the game.

The following $Q$ lines describe the round of the game, the $i$-th line describing the $i$-th round of the game. Each line will contain the integer $T$. In the case when $T$ is equal to 1, it denotes the first type of round and the shown word $P$ follows in the same line, consisting of only lowercase letters of the English alphabet.

In the case when $T$ is equal to 2, it denotes the second type of round and the number $S$ ($1 \leq S \leq N$) follows in the same line, the label of the barbarian whom Tarzan asked the question.

The total length of all words written on the barbarians’ stone tablets will not exceed $2 \cdot 10^6$.

The total length of all words that Tarzan shows the barbarians will not exceed $2 \cdot 10^6$.

-----Output-----
For each round of the second form, output a single line. The $i$-th line must contain the correct answer to Tarzan’s question in the $i$-th round of type 2.

-----Examples-----
Sample Input:
3
a
bc
abc
3
1 abca
2 1
2 3
Sample Output:
1
1
user: John Doe wants to transport his possessions from one bank of Lake Michigan to the other. His possessions consist of $W$ wolves, $S$ sheep, and $C$ cabbages. The transportation will be carried out using a boat that can hold up to $K$ of these items at the same time. During each step, John can take some items from one bank and transfer them to the other bank. Unfortunately, when left unsupervised, wolves will eat sheep and sheep will eat cabbages (but wolves don’t eat cabbages). John doesn’t want to lose his possessions, so he has to devise a scheme such that this doesn’t happen. With John present, any combination of items is allowed (both on the bank and in the boat). This is also true during the loading process. Since John isn’t very good at solving problems like this, he asks you to help him.

-----Input-----
Input contains a single line with four integers: $W$, $S$, $C$, $K$. The input satisfies the following constraints:\[ 0 \leq W, S, C, K \leq 10^6, \]\[ 1 \leq max(W, S, C). \]

-----Output-----
If it’s possible to perform the transportation without the loss of items, print YES, otherwise print NO.

-----Examples-----
Sample Input:
1 1 1 1
Sample Output:
YES
user: It is exam time! You have, of course, been spending too much time participating in various programming contests and have not done much studying. Now you have $N$ subjects to study for, but only a limited amount of time before the final exams. You have to decide how much time to allocate to studying each subject, so that your average grade over all $N$ subjects is maximized. 

As a seasoned programming contest competitor, you recognize immediately that you can determine the optimal allocation with a computer program. Of course, you have decided to ignore the amount of time you spend solving this problem (i.e. procrastinating).

You have a total of $T$ hours that you can split among different subjects. For each subject $i$, the expected grade with $t$ hours of studying is given by the function $f_ i(t) = a_ i t^2 + b_ i t + c_ i$, satisfying the following properties:
 - $f_ i(0) \geq 0$;
 - $f_ i(T) \leq 100$;
 - $a_ i < 0$;
 - $f_ i(t)$ is a non-decreasing function in the interval $[0,T]$.

You may allocate any fraction of an hour to a subject, not just whole hours. What is the maximum average grade you can obtain over all $n$ subjects?

-----Input-----
The first line of each input contains the integers $N$ ($1 \leq N \le 10$) and $T$ ($1 \leq T \le 240$) separated by a space. This is followed by $N$ lines, each containing the three parameters $a_ i$, $b_ i$, and $c_ i$ describing the function $f_ i(t)$. The three parameters are separated by a space, and are given as real numbers with $4$ decimal places. Their absolute values are no more than $100$.

-----Output-----
Output in a single line the maximum average grade you can obtain. Answers within $0.01$ of the correct answer will be accepted.

-----Examples-----
Sample Input:
2 96
-0.0080 1.5417 25.0000
-0.0080 1.5417 25.0000
Sample Output:
80.5696000000
user: Dezider is making a game board for the game of Convexity. He drilled a bunch of holes in a piece of wood. As the name of the game suggests the holes were on the boundary of a convex polygon. After turning over the piece of wood, Dezider froze—he had damaged the famous Picasso lithograph—The Bull No. 8. Now the question is: how to fix the damage? Drawing a bunch of straight lines to cover the holes seems like a good repair method but, of course, Dezider would like to draw as few lines as possible. He needs your help. Write a program that, given the positions of the holes, finds the smallest number of straight lines that can cover the holes.

-----Input-----
The only input line starts with $n$, the number of holes. Then $2n$ numbers, the coordinates of the holes, follow. You can assume that $3 \leq n \leq 1000$ and the coordinates are integers between $-1000000$ and $1000000$. The holes lie on the boundary of a convex polygon.

-----Output-----
The output contains one line with the smallest number $\ell $, such that $\ell $ straight lines can cover the holes.

-----Examples-----
Sample Input:
4 0 0 1 1 1 0 0 1
Sample Output:
2
user: Weenesia is an archipelago of perfectly circular islands in the 2D plane. Many islands have palm trees growing in them, perfectly straight up, so we can represent a tree by a 2D point and a height.

We want to build a courier system in the islands, i.e., we want to be able to move any object from any land point to any other land point. It is possible to move an object within an island without restrictions. It is also possible to climb to a palm tree and throw the object to a distance proportional to the height of the palm tree (or less), and possibly in a different island.

Unfortunately, this may not be enough to reach our goal, so we might want to build a tunnel between two islands. The tunnel connects two points on two islands and may cross under both the sea and other islands. Each of the two entrances of a tunnel must be at least $1$ meter away from the sea to avoid flooding.

Your task is to find the minimum length of a tunnel such that a courier system is possible.

-----Input-----
The first line contains three integers $n$, $m$, and $k$ ($1 \leq n \leq 5000$, $0 \leq m \leq 10000$, $1 \leq k \leq 1000$), the number of islands and palm trees respectively, and the ratio between object throwing range and palm height.

Each of the next $n$ lines contains three integers $x$, $y$, and $r$ ($|x|,|y|\leq 10^6$, $100 \leq r \leq 10^6$), the center and radius of an island, in centimetres. Each of the next $m$ lines contains three integers $x$, $y$, $h$ ($|x|,|y|\leq 10^6$, $1 \leq h \leq 10^4$), the center and height of a palm tree, in centimetres.

No two islands intersect. Each palm tree lies strictly inside an island. No two palm trees grow in the same spot.

-----Output-----
Output the minimum length of a tunnel in centimetres, $0$ if no tunnel is needed, or “impossible” if no such tunnel exists. Answers with an absolute or relative precision up to $10^{-6}$ will be accepted.

-----Examples-----
Sample Input:
3 2 3
0 0 400
1000 0 400
2000 0 400
300 0 150
1300 0 150
Sample Output:
1400
user: Oostende Beach is a very long beach located in the north of Belgium. On this beach, there are $n$ huts located along a straight line. People can rent a room in one of those huts to spend their beach vacations together with the other tenants.

Every day at lunch time, a food truck drives by to serve fries to the guests. The truck parks in front of one of the huts and people form two queues. The people staying in huts to the left of the food truck queue on the left, and the people to the right of the food truck queue on the right. The people staying in the hut in front of the food truck split their group in half, one half going to the left queue and the other half going to the right queue. If this is an odd number of people, the remaining person will go to the queue with fewer people, or choose one randomly if the queues have the same length. The food truck always positions itself so that the difference between the number of people in the left queue and the number of people in the right queue is as small as possible.

Each night the number of guests in exactly one of the huts changes. Can you help the food truck find the best position for each day?

-----Input-----
 - The first line of the input consists of two integers $1\leq n \leq 10^5$, the number of huts, and $1\leq q\leq 10^5$, the number of days.
 - The second line has $n$ integers $a_0$, $\dots $, $a_{n-1}$ satisfying $1\leq a_ i \leq 10^6$ for $0\leq i < n$, where $a_ i$ is the current number of people in hut $i$.
 - Then follow $q$ lines with two integers $0\leq i<n$ and $1\leq x \leq 10^6$. The $j^\textrm {th}$ of these lines indicates that at day $j$ the number of people in hut $i$ changes to $x$.

-----Output-----
 - Print $q$ lines: the optimal position of the food truck after each of the $q$ nights. If there are multiple optimal positions, print the smallest one.

-----Examples-----
Sample Input:
5 4
3 1 3 4 2
0 5
0 9
4 5
2 1
Sample Output:
2
1
2
1
user: Tira would like to join a multiplayer game with $n$ other players. Each player has a character with some features. There are a total of $k$ features, and each character has some subset of them. 

The similarity between two characters $A$ and $B$ is calculated as follows: for each feature $f$, if both $A$ and $B$ have feature $f$ or if none of them have feature $f$, the similarity increases by one.

Tira does not have a character yet. She would like to create a new, very original character so that the maximum similarity between Tira’s character and any other character is as low as possible.

Given the characters of the other players, your task is to create a character for Tira that fulfils the above requirement. If there are many possible characters, you can choose any of them.

-----Input-----
The first line of input contains two integers $n$ and $k$, where $1 \le n \le 10^5$ is the number of players (excluding Tira) and $1 \le k \le 20$ is the number of features.

Then follow $n$ lines describing the existing characters. Each of these $n$ lines contains a string of $k$ digits which are either $0$ or $1$. A $1$ in position $j$ means the character has the $j$’th feature, and a $0$ means that it does not have the $j$’th feature.

-----Output-----
Output a single line describing the features of Tira’s character in the same format as in the input. If there are multiple possible characters with the same smallest maximum similarity, any one of them will be accepted.

-----Examples-----
Sample Input:
3 5
01001
11100
10111
Sample Output:
00010
user: Your friend’s newest hobby is to play movie theme songs on her freshly acquired floppy drive organ. This organ is a collection of good old floppy drives, where each drive has been tampered with to produce sound of a unique frequency. The sound is produced by a step motor that moves the read/write head of the floppy drive along the radial axis of the drive’s spin disk. The radial axis starts in the center of the spin disk and ends at the outer edge of the spin disk.

The sound from one drive will play continuously as long as the read/write head keeps moving in one direction; when the head changes direction, there is a brief pause of $1$fs—one floppysecond, or about $100$ microseconds. The read/write head must change direction when it reaches either the inner or the outer end point of the radial axis, but it can also change direction at any other point along this axis, as determined by your friend. You can make the head stay still at any time and for as long as you wish. The starting position of the read-write head can be chosen freely.

Your friend is a nutcase perfectionist, and will not accept any pauses where there are not supposed to be any; nor will she accept sound when there is meant to be silence. To figure out whether a given piece of music can be played—perfectly—on her organ, she has asked for your help.

For each frequency, you are given a list of intervals, each describing when that particular frequency should play, and you must decide if all of the frequencies can be played as intended. You can assume your friend has enough drives to cover all the required frequencies.

-----Input-----
The first line contains an integer $f, 1 \leq f \leq 10$, denoting the number of frequencies used. Then follow $f$ blocks, on the format:
 - A single line with two integers $t_ i, 1\leq t_ i \leq 10\ 000$ and $n_ i, 1\leq n_ i \leq 100$; the number of floppyseconds it takes for the read/write head of frequency $i$ to move between the end points of its radial axis, and the number of intervals for which frequency $i$ should play.
 - $n_ i$ lines, where the $j$-th line has two integers $t_{i,2j}, t_{i,2j+1}$, where $0\leq t_{i,2j},t_{i,2j+1} \leq 1\ 000\ 000$, indicating that the $i$-th frequency should start playing at time $t_{i,2j}$ and stop playing at time $t_{i,2j+1}$. You can assume that these numbers are in stricly ascending order, i.e. $t_{i,1} < t_{i,2} < \dots < t_{i, 2n_ i}$.

-----Output-----
If it is possible to play all the $f$ frequencies as intended, output “possible”. Otherwise output “impossible”.

-----Examples-----
Sample Input:
1
6 2
0 4
6 12
Sample Output:
possible