meetforever/GRPO_CL huggingface dataset:
user: Bob’s green thumb has recently gotten him a job as a gardener at a local park. Along with caring for all the plants in the garden, he was also given the responsibility of completely redesigning the park with all new equipment and green spaces.

Unfortunately for Bob, he’s not as good at financing as he is at gardening, and may have messed up. In one area of the garden, he has a courtyard in the shape of a perfect square. In the process of designing the courtyard, he spent so much money on fertilizer and grass seed that he had to buy cheap sprinklers.

When the time came to install the sprinklers, Bob found out that the sprinklers don’t all rotate the same amount, and not all of the grass is getting water. Assuming that each sprinkler can spray water infinitely far, help Bob determine the proportion of the courtyard that is watered by the sprinklers.

-----Input-----
The input consists of a single line containing four real numbers $a$, $b$, $c$, and $d$ ($0\leq a, b, c, d\leq 90$) representing the sizes of four angles in degrees. The number $a$ represents the angle that the bottom right sprinkler rotates from the right wall; similarly, $b$ is the angle that the top right sprinkler rotates from the top wall, $c$ is the angle that the top left sprinkler rotates from the left wall, and $d$ is the angle that the bottom left sprinkler rotates from the bottom wall. All numbers will be given with no more than $3$ digits after the decimal point.

-----Output-----
Output the proportion of the area of the courtyard that is watered by the sprinklers as a real number. Your answer will be considered correct if it is within $10^{-6}$ of the correct answer.

-----Examples-----
Sample Input:
45 45 0 0
Sample Output:
0.75
user: The prudent Mr. Day and adventurous Dr. Knight have decided to be backpack buddies and go trekking in the gorgeous Norwegian mountains. Of course they will use the trails marked by the Norwegian Trekking Association (DNT), like any sane trekkers would; such trails all start and end at some cabin where it is possible to lay over. Mr. Day for one likes sleeping comfortably, so he immediately suggested that they sleep in a cabin every night.

However, Dr. Knight was of a different opinion; she argued that they’d arrive at their destination much quicker if they went for as long as possible each day, and then slept in tents in between two cabins if need be. Even though Mr. Day agreed that reaching the destination as quickly as possible was desirable, he was not willing to sacrifice the comfort of a proper bed.

After a fierce argument, Mr. Day and Dr. Knight decided to split up, each to follow their own strategy. Assuming they both walk at the same pace, how long will Dr. Knight need to wait at the final destination before Mr. Day shows up?

-----Input-----
The first line of input contains two integers, $n$ ($1 \leq n \leq 100000$) the number of cabins, and $m$ ($1 \leq m \leq 100000$) the number of trails. Then follows $m$ lines, each describing a trail. The $i$’th such line contains three integers, $u_ i$, $v_ i$ and $d_ i$ ($0 \leq u_ i, v_ i < n$, $0 \leq d_ i \leq 12$) meaning that there is a trail between cabin $u_ i$ and cabin $v_ i$ which will take exactly $d$ hours to traverse. (There can be more than one trail between two cabins, and some trails could lead back to the same cabin from where it started).

Mr. Day and Dr. Knight start in cabin $0$ and their destination is cabin $n-1$. Each day they start walking at 08:00 in the morning, and then walks non-stop for (at most) $12$ hours before settling down for the night.

-----Output-----
Output a single integer, the number of hours Dr. Knight needs to wait at the destination before Mr. Day shows up.

-----Examples-----
Sample Input:
5 6
0 1 2
0 3 8
1 2 11
2 3 5
2 4 2
4 3 9
Sample Output:
4
user: Jack the Lumberjack used to love chopping down trees. Jack is getting older and is becoming tired of this activity he used to love. He thinks of an idea, ‘The Big One’, and fantasizes about going out into the forest one last time to harvest as many trees as possible.

Jack calls the forest administrator for his local evergreen forest. The forest administrator tells him about how the population changes for each species of tree. For each species $k$, $S_ k$ trees are planted in year $B_ k$. For the next $Y_ k$ years, the population increases by $I_ k$ per year. After $Y_ k$ years, it will decrease by the same amount $I_ k$ per year, until possibly dying out.

Armed with this information, Jack wants to figure out the maximum amount of trees that could be harvested at once from now until the future. If he is no longer around to do it, his descendants will be!

Assume all populations change instantly and at the same time, once per year. Jack would assess each population’s size after the yearly change occurred.

-----Input-----
The input contains a single test case. The first line contains an integer $N$ ($1 \le N \le 1000$) representing the number of tree species in the forest.

Each of the following $N$ lines represents a single tree species population. Each of these population lines contains $4$ integer numbers Y I S B ($0 \le Y \le 1000000$, $0 \le I \le 1000$, $0 \le S \le 1000000$, $0 \le B \le 1000000$). where $S$ is the starting population size, $B$ the year in which the population is planted, $Y$ the number of years during which the population increases each year by $I$ before it decreases by $I$ until it (possibly) dies out.

-----Output-----
Print the maximum amount of trees that can be harvested in any single year.

-----Examples-----
Sample Input:
1
10 10 0 5
Sample Output:
100
user: You are given a set of $n$ axis-aligned rectangles in a 2D plane. For this problem, two rectangles are considered to intersect if their boundaries contain any common points (in particular, two nesting rectangles don’t count as intersecting). Determine if some pair of rectangles intersect.

In this example, only rectangles A and B intersect.

-----Input-----
Each test case will begin with a line with a single integer $n$ ($1\! \le \! n\! \le \! 10^5$), which is the number of rectangles.

Each of the next $n$ lines will contain four space-separated integers:$x_1$ $y_1$ $x_2$ $y_2$

($-10^9\! \le \! x_1,y_1,x_2,y_2\! \le \! 10^9, x_1\! <\! x_2, y_1\! <\! y_2$), which describe a rectangle, where $(x_1,y_1)$ is the lower left corner and $(x_2,y_2)$ is the upper right corner. All $x$ values will be distinct. All $y$ values will be distinct.

-----Output-----
Output a single integer, which is $1$ if some pair of rectangles intersect, $0$ if no pair of rectangles intersect.

-----Examples-----
Sample Input:
3
0 0 2 2
1 1 3 4
5 7 6 8
Sample Output:
1
user: Peter is attempting to deep-water solo a rock climbing cliff over the ocean. Deep-water soloing (DWS) is a form of solo rock climbing that relies solely upon the presence of water at the base of the climb to protect against injury from falling.

Rock climbing is very exhausting and takes lots of energy. Since Peter is not very flexible, he can only move $1$ unit in any of the four directions: Up, Down, Left, and Right. Traveling to a different square will decrease Peter’s energy by the amount on that square. Note that the amount of energy on a square can be negative. In this case, Peter will gain energy.

If Peter’s energy is negative, he will fall into the water.

Peter doesn’t want to get wet, so he asks you to compute the minimum amount of energy he needs to complete the climb, assuming he takes an optimal route.

-----Input-----
The first line of the input will contain two integers, $R$, $C$ ($1 \leq R, C \leq 15$). The second line of input will consist of a row of $C$E characters, separated by spaces, representing the top of the cliff. These take $0$ units of energy to enter. Peter can choose any of them.

Next, there will be $R$ rows of $C$ columns of numbers $X_{r,c}$, where ($-9 \leq X_{r,c} \leq 9$), the energy required to enter that section of cliff. The final line of input will consist of a row of $C$ S characters, representing the possible start points of the climb. These take $0$ units of energy to enter. Peter may return to any field, including the starting position, as often as he likes.

-----Output-----
Output a single integer, the minimum initial amount of energy necessary to complete the climb without falling.

-----Examples-----
Sample Input:
5 5
E E E E E
1 2 3 4 5
5 4 3 2 1
-2 -2 -2 -2 -2
8 8 8 8 8
9 9 9 9 9
S S S S S
Sample Output:
17
user: Alan works for a company specialising in computer security. He recently came up with what he thinks is a great public key cryptosystem, in which the private key consists of two permutations $\pi $ and $\sigma $ of $\{ 1, \dots , n\} $. The public key $(a_1, \dots , a_ n)$ is then given by $a_ i \equiv \pi _ i + \sigma _ i \pmod{n}$ for $1 \leq i \leq n$. The expression $x \equiv y \pmod n$ means that $x$ and $y$ have the same remainder after division by $n$.

As an example with $n = 5$, consider\begin{align*} \pi & = (3,1,5,2,4), \\ \sigma & = (5,1,3,4,2), \text {and} \\ a & = (3,2,3,1,1). \end{align*}

Here, for example, $a_5 \equiv 1 \equiv 4 + 2 \equiv \pi _5 + \sigma _5 \pmod{5}$, and all the entries in $\pi $ and $\sigma $ respectively are $\{ 1, \dots , 5\} $, each number occurring exactly once.

Alan’s coworkers have some doubts about this system being secure, since finding any private key corresponding to the public key would break the system. Your task is to help them out. Given $n$ and a sequence $a = (a_1, \dots , a_ n)$, determine whether there are two permutations $\pi $ and $\sigma $ such that $\pi _ i + \sigma _ i = a_ i \pmod{n}$ for each $i$. If there are more such pairs, print any of them.

-----Input-----
The first line contains the length $n$ of the sequence and the permutation is written. The second line contains integers $a_1, \dots , a_ n$, satisfying $1 \leq a_ i \leq n$. The length $n$ satisfies $1 \leq n \leq 1000$.

-----Output-----
If there is no solution, output “impossible”. If there is a solution, output any of them, writing the two permutations on one line each.

-----Examples-----
Sample Input:
5
3 2 3 1 1
Sample Output:
1 4 3 5 2 
2 3 5 1 4
user: A crazed boar has become lost in the forest! In its madness, it will charge in a random direction at blazing speed, until it has traveled a distance $d$, or until it hits a tree (in which case the boar will become dazed and end its charge), whichever comes first. Given the layout of trees around the boar, what is the probability the boar completes its wild charge without hitting a tree?

We will model the forest as the $xy$ plane, with the boar a disk of radius $b$ that begins centered at the origin $(0,0)$. We will also represent the trees as disks, with varying radii $r_ i$ and centers $(x_ i, y_ i)$. The boar charges by choosing a direction uniformly at random, and then translating in that direction for a distance $d$. The boar hits a tree and becomes dazed if, at any point during its charge, the boar’s body has nonzero area of overlap with any tree.

-----Input-----
The first line of input contains a single integer $n$ $(0 \leq n \leq 10000)$, the number of trees in the forest. $n$ lines follow, each of which contain three integers $x_ i$, $y_ i$, and $r_ i$, denoting the position and radius of the $i$th tree. These inputs satisfy $-10^6 \leq x_ i, y_ i \leq 10^6$ and $0 < r_ i \leq 10^6$. The final line of input contains two integer $b$ and $d$, the radius of the boar $(0 < b \leq 10^6)$ and the distance that the boar will charge $(0 \leq d \leq 10^6)$. You may assume that no tree overlaps with or touches the boar at the start of its charge (but trees might overlap or touch each other).

-----Output-----
Print a single real number: the probability that the boar completes its charge without hitting any tree. Your answer will be considered correct if it has absolute or relative error at most $10^{-6}$.

-----Examples-----
Sample Input:
1
3 0 1
1 4
Sample Output:
0.76772047
user: Žofka invented a new word puzzle. She gives you two strings $s_1$ and $s_2$ of the same length. You need to modify $s_1$ into $s_2$ as quickly as possible. The trick is that you are allowed to modify the strings only using the following types of moves: (1) shift forward where you choose a substring of one of the strings and shift each of its letters by 1 forward in the alphabet, or (2) shift backward where you shift each letter in a substring backward in the alphabet. The first move is not allowed if the substring contains the letter z while the second move is not allowed if the subtring contains a. What is the smallest number of moves you need to modify $s_1$ into $s_2$?

-----Input-----
Each word puzzle is described on a single line that contains the strings $s_1$ and $s_2$ separated by space. The strings contain only lower case letters. You may also assume that the length of each string is at most $10000000$.

-----Output-----
Output one line with the smallest number of moves needed to modify $s_1$ into $s_2$.

-----Note-----
The first sample input can be modified in the following way. First shift lo forward, getting helmp. Then shift h forward 12 times, getting telmp. Then shift l 11 times backward to get teamp and then shift p forward three times to get teams. Total number of moves is $1+12+11+3=27$.

The second sample input can be modified as follows. First shift the entire string forward, getting bbdddbbbb. Then shift ddd backward twice to get bbbbbbbbb. This requires 1+2=3 moves.

-----Examples-----
Sample Input:
hello teams
Sample Output:
27
user: In ancient times, communication was not as swift as it is today. When a kingdom was at war, it could take months to muster all the armed forces. But by using fire-lit beacons at strategic locations, it was still possible to quickly send emergency signals.

When the first beacon is lit, all other beacons within sight from it are also lit. All beacons within sight of these are then lit, and so on until all beacons are lit - assuming of course that all beacons are within sight of each other, directly or indirectly. If they are not, the dire news must be carried by riders between some beacons.

Given the location of all beacons in the kingdom as well as the location and size of all mountain peaks, write a program that determines how many messages must be sent by riders in order for all beacons to be lit when an enemy threatens the country.

For simplicity, we model the country in the following way: a beacon is represented as a point in the xy-plane and a mountain peak is represented as a circle. Two beacons are considered to be within sight of each other if no mountain peak blocks the straight line between the two beacons.

The input will be constructed so that the straight line between any pair of beacons will not touch the circumference of a mountain peak, unless it passes through the interior of another mountain peak. Mountain peaks will not overlap or touch, nor will any beacon be on a mountain peak or on its circumference.

-----Input-----
The first line in the input contains two integers $n$ ($1 \leq n \leq 1000$) and $m$ ($0 \leq m \leq 1000$) the number of beacons and the number of mountain peaks, respectively. Then follow $n$ lines specifying the locations of the beacons. The location of each beacon is given as a pair of integers $x$ and $y$ ($0 \le x, y \le 10000$). Then follow $m$ lines describing the mountain peaks. Each mountain peak is given as a pair of integers $x$ and $y$ ($0 \le x, y \le 10000$) specifying the location of the peak and a radius $r$ ($1 \le r \le 5000$).

-----Output-----
The output should be a single integer: the number of messages that must be carried by riders for all beacons to be lit.

-----Examples-----
Sample Input:
6 3
1 8
5 4
7 7
9 2
16 6
17 10
4 7 2
6 3 1
12 6 3
Sample Output:
2
user: Consider $n$ initial strings of lower case letters, where no initial string is a prefix of any other initial string. Now, consider choosing $k$ of the strings (no string more than once), and concatenating them together. You can make this many such composite strings:$n \times (n-1) \times (n-2) \times \ldots \times (n-k+1)$

Consider sorting all of the composite strings you can get via this process in alphabetical order. You are given a test composite string, which is guaranteed to belong on this list. Find the position of this test composite string in the alphabetized list of all composite strings, modulo $10^9+7$. The first composite string in the list is at position $1$.

-----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, first $n$ and then $k$ ($1 \le k \le n$), where $n$ is the number of initial strings, and $k$ is the number of initial strings you choose to form composite strings. The upper bounds of $n$ and $k$ are limited by the constraints on the strings, in the following paragraphs.

Each of the next $n$ lines will contain a string, which will consist of one or more lower case letters $a..z$. These are the $n$ initial strings. It is guaranteed that none of the initial strings will be a prefix of any other of the initial strings.

Finally, the last line will contain another string, consisting of only lower case letters $a..z$. This is the test composite string, the position of which in the sorted list you must find. This test composite string is guaranteed to be a concatenation of $k$ unique initial strings.

The sum of the lengths of all input strings, including the test string, will not exceed $10^6$ letters.

-----Output-----
Output a single integer, which is the position in the list of sorted composite strings where the test composite string occurs. Output this number modulo $10^9+7$.

-----Examples-----
Sample Input:
5 3
a
b
c
d
e
cad
Sample Output:
26
user: The premier of the anticipated action film No Thyme to Fry is right around the corner, and it is time to give early screenings to film critics so that they can review it. A small cinema has been selected to show these early screenings. 

There are $n$ critics numbered from $1$ to $n$ scheduled to watch the movie early, and each of them will watch it separately. After watching it, they will immediately give it a score from $0$ to $m$. Susan, the cinema owner, has carefully looked at every critic’s social media and already knows that the $i$th critic thinks the movie is worth a score of $a_ i$. However, the $i$th critic will not simply give the movie a score of $a_ i$ like you would expect, because they also take into account the scores that the other critics gave. Here is how they behave:
 - The first critic to arrive will be so happy that they are the first to review the movie that they will give it a score of $m$ regardless of their initial opinion.
 - Every subsequent critic will look at the average score given by the previous critics. If this number is smaller than or equal to the initial opinion $a_ i$ then the critic will give it a score of $m$, otherwise they will give it a $0$.

Susan thinks the critics’ behaviour is ridiculous. She has watched the movie, and it is clearly worth a score of exactly $k/n$ and nothing else! But Susan is the owner of the cinema, so she gets to decide in what order to invite the critics. Your task is to find a permutation of $1,2, \dots , n$ so that if the critics arrive in this order the average score will be exactly $k/n$.Input

The first line of input contains three integers $n$, $m$ and $k$ ($1 \leq n \leq 2 \cdot 10^5$, $1 \leq m \leq 10^4$, $0 \leq k \leq n \cdot m$). The second line contains the $n$ integers $a_1, a_2, \ldots , a_ n$ ($0 \le a_ i \le m$ for each $i$), the $n$ critic scores as described above.Output

If the critics can be ordered in such a way that the resulting average score is exactly $k/n$, then output $n$ integers $p_1, \ldots , p_ n$ ($1 \le p_ i \le n$), where $p_ i$ indicates that the $i$th critic to visit the cinema is the critic numbered $p_ i$. This list of integers should be a permutation such that the average score given by the critics is $k/n$. If there are multiple solutions any one will be accepted.

Otherwise, if there is no such way to order the critics, output “impossible”.

-----Examples-----
Sample Input:
5 10 30
10 5 3 1 3
Sample Output:
3 5 2 1 4
user: In the cold and remote areas of northern Sweden, a young boy named Anton lives. Being born to a family of pistvakts (an occupation that involves drinking moonshine called “bäverhojt”, hunting bears and occasionally handling safety in the mountains), he has been handed the responsibility of mounting temperature sensors in the Scandinavian Mountains. Anton has to place three identical sensors along the mountain range, which can be modeled as a one-dimensional number line.

A lot of snow fell during the winter, and the sensors need to be placed at points with an ascending order of snow levels, since they work best arranged that way. This means that at the point of the leftmost sensor, the snow level must be strictly less than that of the other sensors, and at the point of the rightmost sensor, the snow level must instead be the strictly higher than that of the other sensors. Anton may also only place sensors at integer points. His house is located at point $0$, and no sensor may be placed to the left of the house.

Even with this limitation, there can be a huge number of ways in which he can place the sensors. Anton has saved the log of where snow has fallen during the winter, given as a number of ranges $[a, b]$, indicating that 1 meter of snow fell between and including points $a$ and $b$. If snow fell $k$ times over a certain point, the snow level in that point is $k$. Can you help him calculate the number of ways he may place the sensors?

-----Input-----
The first line of input contains a number $0 \le n \le 10^5$, the number of entries Anton has in his snow log. Then follow $n$ lines, each containing the two numbers $0 \le a \le b \le 10^{18}$, denoting an interval in which snow fell.

-----Output-----
Output consists of a single integer – the number of ways in which Anton can place the sensors. This number may be large, so output the remainder modulo $1000000009$. If there is no way Anton can place the sensors, you should instead output the string “shovel time!”, since Anton then must take his snowmobile and manually construct three points with the sought property.

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