meetforever/GRPO_CL huggingface dataset:
user: Punctual City is well known for the punctuality of its citizens and its public transportation system. It is particularly famous for its train system. It is always on time, and never too late (or even too early). Statistics about train boarding is regularly collected to keep things running smoothly.

A train has cars numbered $1$ to $N$ (from front to back), each of length $L$ meters. Each car has exactly one door for boarding located at the center ($L/2$ meters from each end of the car). There are no gaps between cars.

When the train stops at the boarding platform, each passenger waiting for the train walks to the door of the car which is closest to them, taking the higher numbered car in the case of a tie.

Given the location of the passengers relative to the train, help the city by reporting the longest distance that any passenger has to walk and the maximum number of passengers boarding any single car.

-----Input-----
The first line of input contains three integers $N$ ($1 \leq N \leq 100$), which is the number of cars of the train, $L$ ($2 \leq L \leq 100$), which is the length of each car, and $P$ ($1 \leq P \leq 1000$), which is the number of passengers waiting for the train. It is guaranteed that $L$ is an even number.

The next $P$ lines describe the location of the passengers relative to the train. Each line contains a single integer $x$ ($0 \leq x \leq 10000$), which is the distance the passenger is behind the front-end of the train.

-----Output-----
Display the longest distance that any passenger has to walk on one line. On the next line, display the maximum number of passengers boarding any single car.

-----Examples-----
Sample Input:
68 90 6
3809
288
2306
2215
4211
379
Sample Output:
27
1
user: There is a long electrical wire of length $\ell $ centimetres between two poles where birds like to sit. After a long day at work you like to watch the birds on the wire from your balcony. Some time ago you noticed that they don’t like to sit closer than $d$ centimetres from each other. In addition, they cannot sit closer than 6 centimetres to any of the poles, since there are spikes attached to the pole to keep it clean from faeces that would otherwise damage and weaken it. You start wondering how many more birds can possibly sit on the wire.

-----Task-----
Given numbers $\ell $ and $d$, how many additional birds can sit on the wire given the positions of the birds already on the wire? For the purposes of this problem we assume that the birds have zero width.

-----Input-----
The first line contains three space separated integers: the length of the wire $\ell $, distance $d$ and number of birds $n$ already sitting on the wire. The next $n$ lines contain the positions of the birds in any order. All number are integers, $1\leq \ell , d\leq 1000000000$ and $0\leq n\leq 20000$. (If you have objections to the physical plausibility of fitting that many birds on a line hanging between two poles, you may either imagine that the height of the line is 0 cm above ground level, or that the birds are ants instead.) You can assume that the birds already sitting on the wire are at least 6 cm from the poles and at least $d$ centimetres apart from each other.

-----Output-----
Output one line with one integer – the maximal number of additional birds that can possibly sit on the wire.

-----Examples-----
Sample Input:
22 2 2
11
9
Sample Output:
3
user: This problem is an extension of another Kattis problem - backspace. In that problem, every time we see a character ‘<’, it actually means that the ‘Backspace’ key is pressed and we undo the last character that was just typed.


The extension is as follows: Now, pressing a ‘<’ (the ‘Backspace’ key) when the (typing) cursor is at the front of the line does nothing. Now if we see a character ‘[’, it actually means that the ‘Home’ key is pressed and we move the (typing) cursor to the front of the line. Similarly, if we see a character ‘]’, it actually means that the ‘End’ key is pressed and we move the (typing) cursor the back of the line. For all other valid character in the input, it actually means that the corresponding key is pressed, we insert that character at the (typing) cursor position, and advance one position to the right the cursor accordingly.

-----Input-----
The input starts with a line containing just one integer $T \: (1 \le T \le 10)$, denoting the number of test cases.


Each test case is a line containing the string that was written in the Text Editor Sim (Steven IMproved). The length of the string is at most $10^{6}$, and it will only contain lowercase letters from the English alphabet [‘$a$’$\; \ldots \; $‘$z$’], digits [‘$0$’$\; \ldots \; $‘$9$’], spaces, as well as some of the three special characters: ‘<’, ‘[’, or ‘]’.

-----Output-----
For each test case, output one line containing the final string that is displayed on screen.

-----Subtasks-----
 - $\textbf{(27.5 points)}$: $1 \le T \le 10$, string length is at most $10^{3}$, there is no ‘[’, as seen in sample $1$.
 - $\textbf{(32.5 points)}$: $1 \le T \le 10$, string length is at most $10^{3}$, there may be ‘[’, as seen in sample $2$.
 - $\textbf{(40 points)}$: $1 \le T \le 4$, string length is at most $10^{6}$.

-----Examples-----
Sample Input:
1
my ]]name]] is]] steva<en]<n halim]]]]]
Sample Output:
my name is steven halim
user: There is a legendary tale about Dragon Balls on Planet X: if one collects seven Dragon Balls, the Dragon God will show up and help you fulfill your wishes.

One day, you are surprised to discover that the tale might possibly be true: you found a Dragon Ball radar at a flea market! The radar shows you the locations of the seven Dragon Balls on Planet X. You want to waste no time checking the truth of the old legend about wish-granting for yourself!

There are $n$ cities in total on the Planet X, numbered from $1$ to $n$. You are currently at city $1$. To travel from one city to another, you can take any of $m$ bidirectional teleport trips, as many times as you like. The $i$-th teleporter costs $t_ i$ coins to use each time, and it can teleport you between cities $a_ i$ and $b_ i$. To collect a Dragon Ball, you simply need to visit the city where it’s located, as indicated on your radar. It is possible that multiple Dragon Balls are at the same city; in this case you pick all of them all up at once if you visit that city.

-----Input-----
The first line of input contains two space-separated integers $n$ and $m$ $(1 \leq n,m \leq 200000)$, the number of cities and possible teleport trips. Then follow $m$ lines containing three space-separated integers $a_ i$, $b_ i$, and $t_ i$ each $(1 \le a_ i, b_ i \le n, 0 \le t_ i \le 10000)$, which, as explained above, represent the two cities connected by the teleport trip, and cost to use the teleporter. Then follows one line of seven space-separated integers, representing the city IDs of the seven Dragon Balls showing on the radar. Each ID $c$ satisfies the bound $1 \leq c \leq n$.

-----Output-----
Print the minimum number of coins that you need to spend to collect all seven Dragon Balls shown on the Dragon Ball radar. If there is no way to complete this task, print $-1$ instead.

-----Examples-----
Sample Input:
10 9
1 2 1
2 3 1
3 4 1
4 5 1
5 6 1
6 7 1
7 8 1
8 9 1
9 10 1
1 2 3 4 5 6 7
Sample Output:
6
user: A water company is trying to provide water from its pumping station to a mansion. The company owns $n$ water stations, numbered $1 \ldots n$, which are connected by a variety of pipes. Water can flow through both directions of a pipe, but the total amount of water that can flow through the pipe is bounded by the capacity of the pipe.

The water company is constantly improving the pipes, increasing the capacity of various pipes. The water company is conducting $k$ improvements (each of which is permanent after it is executed). An improvement consists of taking a pipe between two locations and increasing its capacity by a fixed amount, or installing a pipe between two locations which are not directly connected by a pipe.

After each improvement, the water company wants to know the maximum amount of water the mansion could receive.

-----Input-----
Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. The first line of input contains three integers, $n$ ($2 \le n \le 100$), $p$ ($0 \le p \le \frac{n (n-1)}{2}$), and $k$ ($1 \le k \le 10000$), where $n$ is the number of stations, $p$ is the number of initial pipes, and $k$ is the number of improvements. The first station in the list is always the pumping station, and the second is always the mansion.

The next $p$ lines will describe the pipes in the initial setup. The lines will each contain three integers, $a$, $b$ ($1 \le a < b \le n$) and $c$ ($1 \le c \le 1000$), which indicates that stations $a$ and $b$ are connected by a pipe with capacity $c$. No $(a, b)$ pair will appear more than once in this section.

The next $k$ lines will describe the improvements. The lines will each contain three integers, $a$, $b$ ($1 \le a < b \le n$) and $c$ ($1 \le c \le 1000$), which indicates that the pipe connecting stations $a$ and $b$ has its capacity increased by $c$ (if there is currently no pipe between $a$ and $b$, then one is created with capacity $c$). Note that it is possible for an $(a,b)$ pair to be repeated in this section.

-----Output-----
Output $k+1$ integers, each on its own line, describing the maximum amount of water that can reach the mansion. The first number is the amount of water reaching the mansion in the initial configuration. The next $k$ numbers are the amounts of water reaching the mansion after each improvement.

-----Examples-----
Sample Input:
3 2 1
1 3 10
2 3 1
2 3 15
Sample Output:
1
10
user: In fantasy hockey, there are $n$ team owners that each selects $k$ hockey players. To determine which owner gets which players, the owners hold a draft.

The draft proceeds as follows: the first owner may select any player, then the second owner can select any player except the player taken first and so on. In general, the current owner may take any player that has not been taken previously. Once all owners have selected one player, they repeat this process until all owners have selected $k$ players. No player may be selected by multiple teams.

Initially, all players are given a ranking based on how well they played in the previous year. However, the owners may not agree with this order. For example, the first owner may believe that the player which was ranked third in the previous year is the best player and would prefer to take them.

Each owner has a preference list. On their turn, the owner selects the player that is the highest available player on their own preference list. If all players on their preference list are taken, then they resort to using the ordering from the previous year.

Given the preference list of each owner and the rankings from the previous year, which players did each owner get?

-----Input-----
The first line of the input contains two integers $n$ ($1 \leq n \leq 60$), the number of owners, and $k$ ($1 \leq k \leq 1000$), the size of each team.

The next $n$ lines contain owners’ preferences in the order of drafting. Each line starts with an integer $q_ i$ ($0 \leq q_ i \leq 1500$), the size of the $i^\textrm {th}$ owners’ preference list. $q_ i$ names follow, separated by spaces, in order of $i^\textrm {th}$ owner’s preference. No name appears more than once in the $i^\textrm {th}$ owners’ list.

The next line contains a single integer $p$ ($n \cdot k \leq p \leq 65000$), indicating the number of players in the draft.

The next $p$ lines each contain a single name, they are ordered by their previous year’s ranking. Each player name is unique and comprised of at most $12$ letters of English alphabet.

The names in owners’ preference lists are guaranteed to appear in the player list.

-----Output-----
Display $n$ lines. The $i^\textrm {th}$ of which contains the $k$ names of the players that were selected by the $i^\textrm {th}$ owner. The $n$ teams should be in the original order of owners and players should be listed in the order in which they were drafted following the rules above.

-----Examples-----
Sample Input:
2 2
0
0
6
Shoresy
Jonesy
Reilly
Sholtzy
Fisky
Yorkie
Sample Output:
Shoresy Reilly
Jonesy Sholtzy
user: A family of $n$ gnomes likes to line up for a group picture. Each gnome can be uniquely identified by a number $1..n$ written on their hat.

Suppose there are $5$ gnomes. The gnomes could line up like so: $1, 3, 4, 2, 5$.

Now, an evil magician will remove some of the gnomes from the lineup and wipe your memory of the order of the gnomes. The result is a subsequence, perhaps like so: $1, 4, 2$.

He then tells you that if you ordered all permutations of $1..n$ in lexicographical order, the original sequence of gnomes is the first such permutation which contains the remaining subsequence. Your task is to find the original sequence of gnomes.

-----Input-----
Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. Each test case will begin with a line with two integers $n$ and then $m$ ($1 \le m \le n \le 10^5$), where $n$ is the number of gnomes originally, and $m$ is the number of gnomes remaining after the evil magician pulls his trick. Each of the next $m$ lines will contain a single integer $g$ ($1 \le g \le n$). These are the remaining gnomes, in order. The values of $g$ are guaranteed to be unique.

-----Output-----
Output $n$ lines, each containing a single integer, representing the first permutation of gnomes that could contain the remaining gnomes in order.

-----Examples-----
Sample Input:
5 3
1
4
2
Sample Output:
1
3
4
2
5
user: These days, many carmakers are developing cars that run on electricity instead of gasoline. The batteries used in these cars are generally very heavy and expensive, so designers must make an important tradeoffs when determining the battery capacity, and therefore the range, of these vehicles. Your task is to help determine the minimum range necessary so that it is possible for the car to travel between any two cities on the continent.

The road network on the continent consists of cities connected by bidirectional roads of different lengths. Each city contains a charging station. Along a route between two cities, the car may pass through any number of cities, but the distance between each pair of consecutive cities along the route must be no longer than the range of the car. What is the minimum range of the car so that there is a route satisfying this constraint between every pair of cities on the continent?

-----Input-----
The first line of the input contains two nonnegative integers $n$ and $m$, the number of cities and roads. Each of these integers is no larger than one million. The cities are numbered from 0 to $n-1$. The first line is followed by $m$ more lines, each describing a road. Each such line contains three non-negative integers. The first two integers are the numbers of the two cities connected by the road. The third integer is the length of the road, a positive integer no larger than $10^9$.

-----Output-----
For each road network, output a line containing one integer, the minimum range of the car that enables it to drive from every city to every other city. If it is not possible to drive from some city to some other city regardless of the range of the car, instead output a line containing the word IMPOSSIBLE.

-----Examples-----
Sample Input:
3 3
0 1 3
1 2 4
2 1 5
Sample Output:
4
user: Arithmetic coding is a method to represent a message as a real number $x$ such that $0 \leq x < 1$. We will assume that the message consists only of uppercase ‘A’s and ‘B’s. The two letters have associated probabilities $p_ A$ and $p_ B = 1 - p_ A$ such that $0 < p_ A < 1$.

The current interval $[a,b)$ is initially set to $[0,1)$ and we will update this interval one letter at a time. To encode a letter, the current interval is divided into two subintervals as follows. Let $c = a + p_ A(b-a)$. If the next letter is ‘A’, $[a,c)$ becomes the current interval. Otherwise, the current interval is now $[c,b)$. This process is repeated for each letter in the message. If $[k,\ell )$ is the final interval, the encoded message is chosen to be $k$.

For example, if the original message is “ABAB” and $p_ A = p_ B = 0.5$, the sequence of intervals encountered in the algorithm is\[ [0,1) \xrightarrow {A} [0, 0.5) \xrightarrow {B} [0.25, 0.5) \xrightarrow {A} [0.25, 0.375) \xrightarrow {B} [0.3125, 0.375). \]

The encoded message is therefore 0.3125, or 0.0101 in binary.

Given the length of the message, the probabilities, and the encoded message, determine the original message.

-----Input-----
The first line contains the integer $N$ ($1 \leq N \leq 15$), which is the length of the original message. The second line contains the integer $D$ ($1 \leq D \leq 7$), which indicates that $p_ A = \frac{D}{8}$. The third line contains the binary representation of the encoded message. It is guaranteed that the binary representation of the encoded message starts with “0.” and contains at most $3N+2$ characters.

It is guaranteed that the encoded message came from an initial message of length $N$ consisting only of ‘A’ and ‘B’ using this value of $p_ A$.

-----Output-----
Display the original message.

-----Examples-----
Sample Input:
4
4
0.0101
Sample Output:
ABAB
user: You have a 2D rectangular grid. Each grid cell contains either an apple, an obstacle, or is empty. Empty cells are denoted as ’.’, apples as ’a’, and obstacles as ’#’. You are to implement a simulation of gravity, based on the following rules: 
 - The obstacles do not move.
 - Whenever there is an empty cell immediately below an apple, the apple moves into the empty cell.

Print out the final configuration of the board after all apples reach their final locations. Merely iterating the gravity rule, a step at a time, will likely take too long on large datasets.

-----Input-----
The input begins with a line containing integers $R$ and $C$, designating the number of rows and columns of the grid, such that $1 \leq R \leq 50000$ and $1 \leq C \leq 10$. The first line is followed by $R$ additional lines, each designating a row of the grid, from top to bottom. Each line has $C$ characters, each of which is either ’.’, ’a’, or ’#’.

-----Output-----
Output $R$ grid lines displaying the final state.

-----Examples-----
Sample Input:
3 3
aaa
#..
..#
Sample Output:
a..
#.a
.a#
user: Walter was once a promising chemist. Now he teaches high school students chemistry, and was recently diagnosed with lung cancer. In both desperation and excitement he decides to use his chemistry skills to produce illegal drugs and make quick money for his family. He forms a partnership with one of his old students, Jesse, who has some experience with the drug scene.

Now Walter and Jesse are preparing for their first “cook” (the process of making the drugs). They have a list of items they need for the cook, but they realized they have to be very careful when going to the store. The reason is that it may be suspicious to buy certain pairs of items, like cold medicine and battery acid, in the same trip.

They decide to divide the items among themselves, so that each of them can go one trip to the store and buy their share of items without the risk of anyone becoming suspicious. Help them find such a division, or tell them that it is not possible.

-----Input-----
The first line of input contains an integer $N$, $1 \leq N < 100000$, the number of items they want to buy. The following $N$ lines contain the names of these items, all of which are different. A name consists of at most $20$ lowercase letters from the English alphabet or underscores, and is non-empty. The next line of input contains an integer $M$, $0 \leq M < 100000$, the number of pairs of items that are considered suspicious when bought together. Then follow $M$ lines, each containing the names of two different items that form a suspicious pair. Each suspicious pair will be listed exactly once.

-----Output-----
If it is possible for Walter and Jesse to divide the items among themselves, then output two lines. In the first line output the names of the items that Walter should buy. In the second line output the names of the items that Jesse should buy. If there are multiple solutions, output any of them. If this is not possible, output impossible.

-----Examples-----
Sample Input:
5
battery_acid
drain_cleaner
antifreeze
cold_medicine
lantern_fuel
2
cold_medicine battery_acid
antifreeze lantern_fuel
Sample Output:
lantern_fuel drain_cleaner battery_acid
antifreeze cold_medicine
user: Paul owns a catering company and business is booming. The company has $k$ catering teams, each in charge of one set of catering equipment. Every week, the company accepts $n$ catering requests for various events. For every request, they send a catering team with their equipment to the event location. The team delivers the food, sets up the equipment, and instructs the host on how to use the equipment and serve the food. After the event, the host is responsible for returning the equipment back to Paul’s company. 

Unfortunately, in some weeks the number of catering teams is less than the number of requests, so some teams may have to be used for more than one event. In these cases, the company cannot wait for the host to return the equipment and must keep the team on-site to move the equipment to another location. The company has an accurate estimate of the cost to move a set of equipment from any location to any other location. Given these costs, Paul wants to prepare an Advance Catering Map to service the requests while minimizing the total moving cost of equipment (including the cost of the first move), even if that means not using all the available teams. Paul needs your help to write a program to accomplish this task. The requests are sorted in ascending order of their event times and they are chosen in such a way that for any $i < j$, there is enough time to transport the equipment used in the $i^{th}$ request to the location of the $j^{th}$ request.

-----Input-----
The first line of input contains two integers $n$ ($1 \le n \le 100$) and $k$ ($1 \le k \le 100$) which are the number of requests and the number of catering teams, respectively. Following that are $n$ lines, where the $i^{th}$ line contains $n-i+1$ integers between $0$ and $1000000$ inclusive. The $j^{th}$ number in the $i^{th}$ line is the cost of moving a set of equipment from location $i$ to location $i+j$. The company is at location $1$ and the $n$ requests are at locations $2$ to $n+1$.

-----Output-----
Display the minimum moving cost to service all requests. (This amount does not include the cost of moving the equipment back to the catering company.)

-----Examples-----
Sample Input:
3 2
40 30 40
50 10
50
Sample Output:
80
user: Alice and Bob are playing a game on a simple connected graph with $N$ nodes and $M$ edges.

Alice colors each edge in the graph red or blue.

A path is a sequence of edges where each pair of consecutive edges have a node in common. If the first edge in the pair is of a different color than the second edge, then that is a “color change.”

After Alice colors the graph, Bob chooses a path that begins at node $1$ and ends at node $N$. He can choose any path on the graph, but he wants to minimize the number of color changes in the path. Alice wants to choose an edge coloring to maximize the number of color changes Bob must make. What is the maximum number of color changes she can force Bob to make, regardless of which path he chooses?

-----Input-----
The first line contains two integer values $N$ and $M$ with $2 \le N \le 100000$ and $1 \le M \le 100000$. The next $M$ lines contain two integers $a_ i$ and $b_ i$ indicating an undirected edge between nodes $a_ i$ and $b_ i$ ($1 \le a_ i, b_ i \le N$, $a_ i \not= b_ i$).

All edges in the graph are unique.

-----Output-----
Output the maximum number of color changes Alice can force Bob to make on his route from node $1$ to node $N$.

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