meetforever/GRPO_CL huggingface dataset:
user: You have just completed a brave journey to see The Wizard of Odds, who agrees to grant you any wish, so long as you can complete the following puzzle:

The Wizard starts by telling you two integers: $N$ and $K$. He then secretly selects a number from $1$ to $N$ (inclusive), and does not tell you this number.

Your goal is to correctly guess the secret number. Before guessing, you are allowed to ask $K$ “true/false” questions about the number, for example, “Is the number even?” or “Is the number between $7$ and $10$?”, or “Is the number $17$ or $22$?”, or “Is the number prime?”. And the Wizard will answer with “true” or “false” to each question. The Wizard will always answer honestly. After answering the $K$ questions, you must guess the number. If you win (guess the number correctly), you will be granted your wish; but if the Wizard wins (you guess incorrectly), you will be turned into a flying monkey.

(Formally, you can think of a “question” as a function from $1, 2, \ldots , N$ to true, false, and the Wizard will answer by telling you whether the value of the function is true or false for his secret number.)

Assuming that you have been told $N$ and $K$, can you always exactly determine the Wizard’s secret number (and guarantee that you win) using only $K$ questions?

-----Input-----
The input consists of a single line containing two integers $N$ and $K$ ($2 \leq N \leq 10^{101}$, $0 \leq K \leq N$), separated by a single space.

Note: These inputs might NOT fit into a $64$-bit integer.

-----Output-----
Output “Your wish is granted!” (without the quotes) if it is possible for you to guarantee that you win the game (regardless of the number the Wizard picks). Otherwise, print “You will become a flying monkey!” (without the quotes) if it is not possible.

-----Examples-----
Sample Input:
8 3
Sample Output:
Your wish is granted!
user: Old MacDonald had a farm, and on that farm she had a square-shaped pasture, and on that pasture she had a cow that was prone to escape. So now Old MacDonald wants to set up a fence around the pasture. Given the area of the pasture, how long a fence does Old MacDonald need to buy? 

-----Input-----
The input consists of a single integer $a$ ($1 \le a \le 10^{18}$), the area in square meters of Old MacDonald’s pasture.

-----Output-----
Output the total length of fence needed for the pasture, in meters. The length should be accurate to an absolute or relative error of at most $10^{-6}$.

-----Examples-----
Sample Input:
16
Sample Output:
16
user: You are in charge of a server that needs to run some submitted tasks on a first-come, first-served basis. Each day, you can dedicate the server to run these tasks for at most $T$ minutes. Given the time each task takes, you want to know how many of them will be finished today.

Consider the following example. Assume $T = 180$ and the tasks take $45, 30, 55, 20, 80,$ and $20$ minutes (in order they are submitted). Then, only four tasks can be completed. The first four tasks can be completed because they take $150$ minutes, but not the first five, because they take $230$ minutes which is greater than $180$. Notice that although there is enough time to perform the sixth task (which takes $20$ minutes) after completing the fourth task, you cannot do that because the fifth task is not done yet.

-----Input-----
The input consists of a single test case. The first line contains two integers $n$ and $T$ where $1 \le n \le 50$ is the number of tasks and $1 \le T \le 500$. The next line contains $n$ positive integers no more than $100$ indicating how long each task takes in order they are submitted.

-----Output-----
Display the number of tasks that can be completed in $T$ minutes on a first-come, first-served basis.

-----Examples-----
Sample Input:
6 180
45 30 55 20 80 20
Sample Output:
4
user: Jessica wants to become a javelin thrower, moreover she wants to become a famous one. However, she doesn’t want to train $40$ hours a day. To avoid much training while still becoming famous, she has concocted a plan: make all her javelins gigantic.

As a software developer by day, she knows she needs a minimum viable javelin for testing, but also that you can glue existing things hastily together and get something that works alright.

She has a couple of steel rods next to her bed – as one does – and decides to go to the blacksmith apprentice Jack to get him to fuse them together.

The good thing about Jack is that he’ll fuse the steel rods together for free. But Jack isn’t that good at fusing things together. When fusing two rods, the fused rod will lose $1$ cm of their combined length.

That’s not a problem for Jessica, but she wonders how big her javelin will become if Jack fuses all the rods together.

-----Input-----
The first line consist of an integer $N$, the number of steel rods she has. Then follows $N$ lines, each containing a single integer $l_ i$ representing the length of the steel rod in cm.

-----Output-----
Print out the length of the jumbo javelin Jack has made for her.

-----Limits-----
 - $1 < N \leq 100$
 - $1 \leq l_ i \leq 50$

-----Examples-----
Sample Input:
4
21
34
18
9
Sample Output:
79
user: As the workload of the semester is ramping up you get the task of refilling the fridge in the lab with soda. The fridge has $s$ slots, each with a capacity for $d$ bottles of soda, and you have $n$ new soda bottles to add to the fridge. The sodas currently in the fridge are all nice and cold, but the new ones are not and need to be cooled in the fridge for a while until they are ready to drink. 

You can only refill the fridge from the front, so in an ideal world, you would first take out all the sodas currently in the fridge, then put in the $n$ new ones, and then put the old and cold sodas in front of the new ones. But in an ideal world you would also not have two exams and a homework deadline coming. You are simply way too busy to do all this work.

Instead, you are going to just put the new bottles in the front of the fridge and hope for the best. However, you can still to be clever about which slots to put the new sodas in. Each time a student comes for a soda, they will take one from the front of a uniformly random non-empty slot in the fridge. You decide to add the new bottles to the fridge so as to maximize the probability that all the next $m$ students getting a soda from the fridge will get a cold one.

-----Input-----
The first line of input contains four integers $n$, $m$, $s$ and $d$ ($1 \le n, m, s, d \le 100$), the number of new soda bottles, number of students to optimize for, number of slots in the fridge, and capacity of each slot, respectively. Then follows a line containing $s$ integers $c_1, \ldots , c_ s$ ($0 \le c_ i \le d$ for each $i$), where $c_ i$ is the number of soda bottles currently in slot $i$ of the fridge.

You may assume that there is free space for all the $n$ new bottles in the fridge.

-----Output-----
If there is a chance that all the next $m$ students will get a cold bottle, then output $s$ integers describing a refill scheme for the $n$ soda bottles that maximizes the probability of this happening. The $i^{\text {th}}$ of these $s$ integers indicates how many of the new bottles are placed in the front of slot $i$ in the fridge. If there are multiple optimal refill schemes, output any one of them. Otherwise, if it is impossible for all the next $m$ students to get a cold soda, output “impossible” instead.

-----Examples-----
Sample Input:
5 3 3 4
0 1 4
Sample Output:
2 3 0
user: Mirko has found an old chessboard and a set of pieces in his attic. Unfortunately, the set contains only white pieces, and apparently an incorrect number of them. A set of pieces should contain:
 - One king
 - One queen
 - Two rooks
 - Two bishops
 - Two knights
 - Eight pawns

Mirko would like to know how many pieces of each type he should add or remove to make a valid set.

-----Input-----
The input consists of $6$ integers on a single line, each between $0$ and $10$ (inclusive). The numbers are, in order, the numbers of kings, queens, rooks, bishops, knights and pawns in the set Mirko found.

-----Output-----
Output should consist of $6$ integers on a single line; the number of pieces of each type Mirko should add or remove. If a number is positive, Mirko needs to add that many pieces. If a number is negative, Mirko needs to remove pieces.

-----Examples-----
Sample Input:
0 1 2 2 2 7
Sample Output:
1 0 0 0 0 1
user: We all know that passwords are not very secure unless users are disciplined enough to use passwords that are difficult to guess. But most users are not so careful, and happily use passwords such as “123456”. In fact, there are lists of commonly used passwords that hackers can use for breaking into systems, and these passwords often work. 

You have done a lot of hacking using such lists, and you have a good idea of how likely each password in the list is the correct one (you are very surprised by the number of people using “123456” as their passwords). You have a new account to hack, and you have decided to try each of the passwords in the list one at a time, until the correct one is found. You are absolutely sure that the account you want to hack uses a password in the given list.

What is the expected number of attempts to find the correct passwords, assuming that you try these passwords in the optimal order?

-----Input-----
The first line of input contains a positive integer $N$, the number of passwords in the list. Each of the next $N$ lines gives the password, followed by a space, followed by the probability that the password is the correct one. Each password consists only of alphanumeric characters and is $1$ to $12$ characters long. Each probability is a real number with $4$ decimal places. You may assume that there are at most $500$ passwords in the list, and that the sum of all probabilities equals $1$. No two passwords in the list are the same.

-----Output-----
Output on a single line the expected number of attempts to find the correct passwords using the optimal order. Answers within $10^{-4}$ of the correct answer will be accepted.

-----Examples-----
Sample Input:
2
123456 0.6666
qwerty 0.3334
Sample Output:
1.3334
user: Like all other good drivers, you like to curse, swear and honk your horn at your fellow automobile drivers. Today you’re at the rear of a long line, brooding over the others’ inability to keep proper distance to the car in front. But are you really keeping your own distance?

You have calculated that in order to never have to use your breaks, you must keep a distance to any car $x$ in front of you at least $p(n+1)$ where $n$ is the number of cars between you and $x$, and $p$ is an integer constant determined by which of your cars you are currently driving.

Given the value of $p$ and the current distances (in random order) to each of the cars ahead of you, calculate the minimum distance you should be keeping to the car directly in front, in order to not have to use your breaks.

-----Input-----
First a line with $1 \leq n \leq 100000$ – the number of cars ahead of you – and $1 \leq p \leq 20$ – the deceleration constant.

Then a single line with $n$ unique integers denoting the current distance to each of the cars ahead of you. Each of these integers are in the interval $[1, 10^7]$



-----Output-----
The minimum distance you must keep to the car directly in front, in order to not have to use your breaks.

-----Examples-----
Sample Input:
3 1
1 2 4
Sample Output:
1
user: While on summer camp, you are playing a game of hide-and-seek in the forest. You need to designate a “safe zone”, where, if the players manage to sneak there without being detected, they beat the seeker. It is therefore of utmost importance that this zone is well-chosen.

You point towards a tree as a suggestion, but your fellow hide-and-seekers are not satisfied. After all, the tree has branches stretching far and wide, and it will be difficult to determine whether a player has reached the safe zone. They want a very specific demarcation for the safe zone. So, you tell them to go and find some sticks, of which you will use three to mark a non-degenerate triangle (i.e. with strictly positive area) next to the tree which will count as the safe zone. After a while they return with a variety of sticks, but you are unsure whether you can actually form a triangle with the available sticks.

Can you write a program that determines whether you can make a triangle with exactly three of the collected sticks?

-----Input-----
The first line contains a single integer $N$, with $3 \leq N \leq 20000$, the number of sticks collected. Then follows one line with $N$ positive integers, each less than $2^{60}$, the lengths of the sticks which your fellow campers have collected.

-----Output-----
Output a single line containing a single word: possible if you can make a non-degenerate triangle with three sticks of the provided lengths, and impossible if you can not.

-----Examples-----
Sample Input:
3
1 1 1
Sample Output:
possible
user: Kim’s current obsession is to build towers from ordered sequences of Lego bricks. The towers are built one at a time, brick by brick. The first available brick is the base of the first tower. If the next available brick is wider than the top of the current tower, we say that the current tower is finished and make the brick the base of a new tower. Otherwise, the brick is placed (in an arbitrary fashion) on top of the current tower.

Given the ordering and widths of the bricks, how many towers is Kim going to build?

-----Input-----
An integer $N$ with $1 \leq N \leq 10^5$, followed by a line consisting of $N$ integers $x_ i$, where $1 \leq x_ i \leq 10^6$, corresponding to the width of the bricks in the order they are available.

-----Output-----
A single integer, the number of resulting towers.

-----Examples-----
Sample Input:
10
4 3 3 2 1 2 2 1 1 3
Sample Output:
3
user: You are the coach of the national athletics team and need to select which sprinters should represent your country in the $4 \times 100$ m relay in the upcoming championships. 

As the name of the event implies, such a sprint relay consist of $4$ legs, $100$ meters each. One would think that the best team would simply consist of the $4$ fastest $100$ m runners in the nation, but there is an important detail to take into account: flying start. In the $2$nd, $3$rd and $4$th leg, the runner is already running when the baton is handed over. This means that some runners – those that have a slow acceleration phase – can perform relatively better in a relay if they are on the $2$nd, $3$rd or $4$th leg.

You have a pool of runners to choose from. Given how fast each runner in the pool is, decide which four runners should represent your national team and which leg they should run. You are given two times for each runner – the time the runner would run the $1$st leg, and the time the runner would run any of the other legs. A runner in a team can only run one leg.

-----Input-----
The first line of input contains an integer $n$, the number of runners to choose from ($4 \leq n \leq 500$). Then follow $n$ lines describing the runners. The $i$’th of these lines contains the name of the $i$’th runner, the time $a_ i$ for the runner to run the $1$st leg, and the time $b_ i$ for the runner to run any of the other legs ($8 \le b_ i \le a_ i < 20$). The names consist of between $2$ and $20$ (inclusive) uppercase letters ‘A’-‘Z’, and no two runners have the same name. The times are given in seconds with exactly two digits after the decimal point.

-----Output-----
First, output a line containing the time of the best team, accurate to an absolute or relative error of at most $10^{-9}$. Then output four lines containing the names of the runners in that team. The first of these lines should contain the runner you have picked for the $1$st leg, the second line the runner you have picked for the $2$nd leg, and so on. Any solution that results in the fastest team is acceptable.

-----Examples-----
Sample Input:
6
ASHMEADE 9.90 8.85
BLAKE 9.69 8.72
BOLT 9.58 8.43
CARTER 9.78 8.93
FRATER 9.88 8.92
POWELL 9.72 8.61
Sample Output:
35.54
CARTER
BOLT
POWELL
BLAKE
user: You are the boss of ACM (Air Conditioned Minions), an upstanding company with a single goal of world domination.

The company has $N$ minions. Each minion works evilly from early morning until evening inside a super secret bunker in Helsinki. After much deliberation, you decided to move your headquarters to Singapore. However, unlike Helsinki, Singapore is very hot, so the entire complex must be air conditioned. With strenuous working hours (under minimum wage too), it is imperative that all your minions work under optimal work condition. In particular, all minions must like the temperatures of the rooms they are in.

You are planning to construct several rooms in your new hideout, and assign your minions there. You fix the temperature of each room to any value you want (different rooms may have different temperatures). After you fix the temperatures, you will assign each of your minions to these rooms (a room can hold any number of minions). You want all minions to like the temperatures of their assigned rooms. Each minion likes an interval of temperature, and these preferences will be given to you.

Air conditioners are very expensive to maintain. Thus, you want to construct as few rooms as possible. What is the minimum number of rooms you need to set up such that it would be possible to assign minions to rooms as discussed earlier?

-----Input-----
The first line contains a non-negative integer $2 \leq N \leq 100$, giving the number of minions in your company. The next $N$ lines each describe the temperature preferences of all your minions. The $i$-th line consists of two single space separated integers $L$ and $U$ ($1 \le L \le U \le 2N$), which denotes that the $i$-th minion likes any temperature between $L$ and $U$, inclusively.

-----Output-----
Print an integer denoting the minimum number of rooms you need to construct.Sample Data Explanation

In the first example, one of the possible solutions is to setup two rooms — one with temperature $2$, and another with temperature $5$. The first two minions can be assigned to the first room, while the third minion can be assigned to the second room.

-----Examples-----
Sample Input:
3
1 2
2 4
5 6
Sample Output:
2
user: Now that Snapchat and Slingshot are soooo 2018, the teenagers of the world have all switched to the new hot app called BAPC (Bidirectional and Private Communication). This app has some stricter social rules than previous iterations. For example, if someone says goodbye using Later!, the other person is expected to reply with Alligator!. You can not keep track of all these social conventions and decide to automate any necessary responses, starting with the most important one: the greetings. When your conversational partner opens with he…ey, you have to respond with hee…eey as well, but using twice as many e’s!

Given a string of the form he…ey of length at most $1000$, print the greeting you will respond with, containing twice as many e’s.

-----Input-----
 - The input consists of one line containing a single string $s$ as specified, of length at least $3$ and at most $1000$.

-----Output-----
Output the required response.

-----Examples-----
Sample Input:
hey
Sample Output:
heey
user: Somewhere in a mountainous region of the world is a collection of $n$ villages. Connecting these villages to one another is a series of roads, always running directly between two villages and allowing travel in both directions. Due to the treacherous landscape, building these roads is expensive, so the minimum number of roads have been constructed such that each village can reach every other village via a sequence of roads. 

Trade between these villages is very important, since not every village has access to the same supply of natural resources. Many villages produce the same resource, however, so it is useful for villages to know their relative distance to other villages so that they can choose trading partners to minimize overall trading costs. Note that the distance between two villages $a$ and $b$ is the sum of the lengths of the individual roads on the shortest path that connects $a$ and $b$.

A project has been underway to compute the distance between every pair of villages. This information has been incorporated in a table, along with a map that shows the layout of villages and roads that run between them. You have been assigned the task of distributing the table and map to all the villages for the betterment of the regional economy.

Unfortunately, not long after you were given this task, a gust of wind blew the map right out of your hand and into the countryside. Despite your best efforts of searching for it, you have been unable to locate it. You know that you could visit all the villages to reconstruct the map and THEN start distributing the map and table, but this will take twice as long as the original task and the villages will be very displeased with you. You wonder, maybe it’s possible to reconstruct the map given only the table?

-----Input-----
The first line of input will contain the integer $n$ ($2 \leq n \leq 2500$), the number of villages in this region. The next $n$ lines will contain $n$ integers each. The $j^{\rm th}$ integer of the $i^{\rm th}$ line is the distance from village $i$ to village $j$. All distances are greater than zero unless $i = j$, less than $10^7$, and it is guaranteed that the distance from village $i$ to village $j$ is the same as the distance from village $j$ to village $i$.

-----Output-----
For each test case, output $n-1$ lines with two integers $u$ and $v$ on each line, indicating that there is a road connecting villages $u$ and $v$ in this region. Assume the villages are numbered from $1$ to $n$. Any solution that outputs the original set of roads will be accepted.

-----Examples-----
Sample Input:
4
0 1 1 2
1 0 2 3
1 2 0 3
2 3 3 0
Sample Output:
1 2
1 3
1 4
user: DRM Encryption is a new kind of encryption. Given an encrypted string (which we’ll call a DRM message), the decryption process involves three steps: Divide, Rotate and Merge. This process is described in the following example with the DRM message “EWPGAJRB”:Divide

– First, divide the message in half to “EWPG” and “AJRB”.Rotate

– For each half, calculate its rotation value by summing up the values of each character ($\textrm{A} = 0, \textrm{B} = 1, \ldots , \textrm{Z} = 25$). The rotation value of “EWPG” is $4 + 22 + 15 + 6 = 47$. Rotate each character in “EWPG” $47$ positions forward (wrapping from Z to A when necessary) to obtain the new string “ZRKB”. Following the same process on “AJRB” results in “BKSC”.Merge

– The last step is to combine these new strings (“ZRKB” and “BKSC”) by rotating each character in the first string by the value of the corresponding character in the second string. For the first position, rotating ‘Z’ by ‘B’ means moving it forward 1 character, which wraps it around to ‘A’. Continuing this process for every character results in the final decrypted message, “ABCD”.

-----Input-----
The input contains a single DRM message to be decrypted. All characters in the string are uppercase letters and the string’s length is even and $\leq 15000$.

-----Output-----
Display the decrypted DRM message.

-----Examples-----
Sample Input:
EWPGAJRB
Sample Output:
ABCD