meetforever/GRPO_CL huggingface dataset:
user: Sally and her friends are trying to cross safely from one bank of a raging river to another. Boulders are scattered within the river, with log planks connecting the banks of the river to some of the boulders, and some pairs of boulders to each other.

Sally begins by trying to cross the river first. She starts at the left bank and crosses one plank at a time, with the goal of reaching the right bank. Walking across a plank takes Sally one second. Each time she crosses a plank, that plank becomes unstable and collapses into the river (so that neither Sally nor her friends can use that plank again). After Sally has safely reached the right bank, another friend tries to cross the river, and so on, until everyone who is able to make it has crossed the river.

Given the graph of banks/boulders and planks and the number of people who need the cross the river, what is the smallest amount of total time (in seconds) required for everyone to cross the river safely? If it is impossible for all people to cross, compute the minimum number of people $n$ who must be left behind and print n people left behind.

-----Input-----
The first line of the input contains three integers $P$, $R$, and $L$: the number of people $P$ who must cross the river, the number of boulders $R$ in the river, and the number of logs $L$ spanning boulders/river banks. These integers satisfy $1 \leq P \leq 10$ and $0 \leq R \leq 1000$ and $0 \leq L \leq 1000$.

Then follows $L$ lines, each of which contains two integers $E_1$ and $E_2$ specifying the endpoints on one log. The values for $E_1$ and $E_2$ are in the range $[-2,R-1]$, where $-2$ signifies the left river bank, $-1$ signifies the right river bank, and all other values indicate one of the boulders in the river.

You may assume that every log has two distinct endpoints, and that no two logs span the same pair of boulders/river banks. There is no guarantee that every boulder, or even the right river bank, is reachable from the left river bank.

-----Output-----
If it is possible for all $P$ people to reach the right bank, print a single integer, the minimum total time (in seconds) required for all people to cross.

If some people must be left behind at the left bank, instead print n people left behind, where the integer $n$ is the least number of people who must be left behind.

-----Examples-----
Sample Input:
2 4 7
-2 0
0 -1
-2 1
1 0
2 1
2 3
3 -1
Sample Output:
6
user: Maj loves pickled cucumber (also known as pickles). However, her partner is not as keen on filling a sandwich with pickles. Maj would like to maximize the amount of pickles on a sandwich, while still avoiding being judged by her partner. 

Both Maj’s sandwich and the pickles have a circular shape. The sandwich has radius $s$ cm and the pickles have radius $r$ cm.

Maj has exactly $n$ pickles. She wants to place as many of them as possible on her sandwich, as long as:
 - at most $z \% $ of the area of the sandwich is covered by pickles.
 - no two pickles overlap (but they are allowed to touch).

How many pickles can Maj place on her sandwich?

-----Input-----
The input consists of:
 - one line with the decimal numbers $s$ and $r$ ($1 \le s \le 10$, $0.5 \le r \le s$, at most $6$ digits after the decimal point), the radius of the sandwich and the radius of a pickle, in centimetres.
 - one line with the integers $n$ and $z$ ($1 \le n \le 7$, $0 \le z \le 100$), the number of pickles Maj have, and the maximum area she may cover with them, in percent.

-----Output-----
Output the maximum number of pickles Maj can place on her sandwich. The input will always be constructed such that this number does not change if the radius of the sandwich increases or decreases by $10^{-6}$.

-----Examples-----
Sample Input:
3 1 4 40
Sample Output:
3
user: Moles are tidy and hard-working animals. Our mole likes to keep its underground residence in utmost order, so that everyone living there knows where to find things.

To achieve this, the mole connected rooms with tunnels so that there is a single unique way to get from one room to any other room. The distance between two rooms is the number of halls passed on the way from one to the other.

Despite all the effort, some of the mole’s guests are complaining that it takes too long to walk between certain pairs of rooms.

The mole decided to reconstruct her residence, closing one tunnel and opening a new one, so that the distance between the farthest two rooms is the smallest possible, but so that it is still possible to reach every room from every other room.

Write a program which determines the distance between the farthest two rooms after reconstruction, which tunnel to close and which to open. It is allowed to reopen the same tunnel that is closed, if this results in the minimum farthest distance.

-----Input-----
The first line contains an integer $N$ ($2 \le N \le 300000$), the number of rooms. The rooms are numbered $1$ to $N$.

Each of the next $N-1$ lines contains two integers, the numbers of rooms a tunnel connects.

-----Output-----
Output on separate lines, in order:
 - The distance between the two farthest rooms after reconstruction.
 - A pair of integers representing a previously existing tunnel, which should be closed.
 - A pair of integers, the rooms between which a new tunnel should be opened.

Note: The solution will not necessarily be unique. Output any reconstruction plan which achieves the smallest distance between the farthest two rooms.

-----Examples-----
Sample Input:
4
1 2
2 3
3 4
Sample Output:
2
3 4
4 2
user: A core right in Roman tenancy law was the availability of sunlight to everybody, regardless of status. Good sun exposure has a number of health benefits, many of which were known even in those ancient times.

The first act of a Roman city plan reviewer, then, is to survey the proposed structures to measure how well they distribute this precious resource. Given any one avenue of buildings arranged West-to-East, the number of hours for which each building is exposed to sunlight needs to be determined.

For the purpose of simplicity, the number of hours a building is in sunlight is proportional to the fraction of the $180$ degrees of sky visible from its top. Thanks in no small part to the marvels of ancient engineering (and also to the strict nutritional regimes of old) you may assume each building is infinitesimally thin.

-----Input-----
 - One line containing one integer $N$ ($1 \leq N \leq 2 \cdot 10^5$): the number of buildings.
 - $N$ further lines each containing two space-separated integers $X_ i$ and $H_ i$ ($1 \leq X, H \leq 10^9$), the location and height respectively, in metres, of the $i^{th}$-most building from the west.

-----Output-----
On each of the $N$ lines of output, write one real number to at least 4 decimal places of accuracy: the number of hours for which the peak of the $i$-th building is bathed in sunlight.

-----Examples-----
Sample Input:
4
1 1
2 2
3 2
4 1
Sample Output:
9.0000
12
12.00000
9.0
user: One thing almost all computers have in common, whether it is a simple stack-based calculator, a 6502 powered BBC Micro, or a brand new Android phone, every modern computer requires programs that turn either high-level languages or assembly language into machine code.

UKIEPC recently designed their own processor. While very easy to load programs onto, it is not as complex as some, since it has only one aim: show a number on an innovative laser display board!

The available memory consists of three $8$-bit registers: A, X, and Y, plus an infinite stack. At program start these registers are initialised to unknown values, and the stack is empty.

The processor supports six unique instructions:
 - PH <reg>: push the contents of the register (i.e. A, X, or Y) onto the stack.
 - PL <reg>: pop a value off the stack into the register. The program will terminate if this instruction is called when the stack is empty.
 - AD: pop two values off the stack, and push the lowest $8$ bits of their sum onto the stack.
 - ZE <reg>: set the register equal to zero.
 - ST <reg>: set the register equal to one.
 - DI <reg>: send the value of the register to the laser display board and exit.

Due to memory constraints, the maximum number of instructions that can be written to disk is $40$. Further instructions will not be executed.

Given a number, write a program to output the number on the laser display board.

-----Input-----
 - One line containing an integer $N$ ($0 \le N \le 255$), the number to output.

-----Output-----
 - At most $40$ lines, each containing one valid instruction.

When run in sequence the lines should output the number $N$. The last instruction should be a DI.

-----Examples-----
Sample Input:
2
Sample Output:
ST A
ST X
PH A
PH X
AD
PL Y
DI Y
user: Photography is a deceptively simple subject to the naïve outsider.

In truth, viewing angles, saturation levels, contrast, proper lighting and focusing all play a part. Today, we are most concerned with the problem of focus.

The proudest space telescope of all, Inquisition IV, launched into space over a decade ago and is starting to show its age in the pictures sent back. Not only is the resolution low by modern standards, all images are painfully blurry! Each pixel in the camera viewport is reported as the average of all those around it in an $N \times N$ box, rounded downwards into an integer.

To secure more funding for future research (and, if budget allows it, some lens wipes for the next telescope) you need to prove you know what’s out there, specifically the number of stellar bodies visible to the telescope. As is well-known by now, stellar bodies are very bright: in fact it is guaranteed that each registers as a region of horizontally and vertically connected pixels of total brightness to the sensor, while everything else registers as fully black.

Handily the telescope has framed the entire “scene”, including capturing all of the surrounding blurriness on camera. This means that any pixels outside the capture region can also be considered as totally black.

-----Input-----
 - One line containing three integers $N$, $R$ and $C$ ($1\le N \le 99 \le R, C \le 1000$; $N\equiv 1\mod 2$) indicating the blur box width and rows and columns registered by the camera respectively.
 - Another $R$ lines, each containing $C$ space-separated hexadecimal integers $L_{r,c}$ ($\mathtt{0x0000} \le L_{r,c} \le \mathtt{0xFFFF}$) where a value of $\mathtt{0x0000}$ is total blackness and a value of $\mathtt{0xFFFF}$ is total whiteness.

-----Output-----
A single integer: the number of stellar bodies visible in the snapshot.

-----Examples-----
Sample Input:
1 5 6
0000 FFFF 0000 0000 0000 0000
FFFF FFFF 0000 FFFF FFFF 0000
0000 0000 0000 FFFF 0000 0000
0000 FFFF FFFF FFFF FFFF 0000
0000 0000 0000 0000 0000 0000
Sample Output:
2
user: Yulia works for a metal processing plant in Ekaterinburg. This plant processes ores mined in the Ural mountains, extracting precious metals such as chalcopyrite, platinum and gold from the ores. Every month the plant receives $n$ shipments of unprocessed ore. Yulia needs to partition these shipments into two groups based on their similarity. Then, each group is sent to one of two ore processing buildings of the plant.

To perform this partitioning, Yulia first calculates a numeric distance $d(i, j)$ for each pair of shipments $1 \le i \le n$ and $1 \le j \le n$, where the smaller the distance, the more similar the shipments $i$ and $j$ are. For a subset $S \subseteq \{ 1, \ldots , n\} $ of shipments, she then defines the disparity$D$ of $S$ as the maximum distance between a pair of shipments in the subset, that is,\[ D(S) = \max _{i, j \in S} d(i, j). \]

Yulia then partitions the shipments into two subsets $A$ and $B$ in such a way that the sum of their disparities $D(A) + D(B)$ is minimized. Your task is to help her find this partitioning.

-----Input-----
The input consists of a single test case. The first line contains an integer $n$ ($1 \le n \le 200$) indicating the number of shipments. The following $n - 1$ lines contain the distances $d(i,j)$. The $i^{th}$ of these lines contains $n - i$ integers and the $j^{th}$ integer of that line gives the value of $d(i, i+j)$. The distances are symmetric, so $d(j, i) = d(i, j)$, and the distance of a shipment to itself is $0$. All distances are integers between $0$ and $10^9$ (inclusive).

-----Output-----
Display the minimum possible sum of disparities for partitioning the shipments into two groups.

-----Examples-----
Sample Input:
5
4 5 0 2
1 3 7
2 0
4
Sample Output:
4
user: While walking in grand malls little Elsa likes to play a game she calls “Lava”. This is a simple game using the different colors of the floor tiles as markers for where it is safe to walk and where it is not. The rules of the game say that you’re allowed to walk on white tiles, but not on black tiles. The tiles are square.

Elsa typically plays this game together with her father. As he is an adult and (sometimes) can move over tiles that Elsa cannot, Elsa has decided that she is allowed to move in all directions while her father is only allowed to move along the $2$ axes of the floor tiles, and they are only allowed to take steps up to a certain length. This means in particular that Elsa can move to any tile within the radius of her step length (measured in the usual Euclidean distance).

The goal of this game is to get from store $A$ to store $B$ as quickly as possible. Both players move at the same time and they are not allowed to do the next move until they are both finished with the first move. As both the father and Elsa hate to lose, the best outcome is to end up with them getting to the finish at the same time. The father would not like to participate in a game where Elsa will lose, or a game where her father can be seen as trying to lose on purpose (Elsa always knows). A player who can’t reach the goal obviously loses.

-----Input-----
The fist line of the input is a line consisting of $2$ integers $A$ and $F$ indicating the maximum step length of Elsa and the maximum step length of the father respectively. The step lengths are given as multiples of a tile width.

 Then follows a line with $2$ integers $L$ and $W$ indicating the length and width of the map of their possible Lava game.

 Then follow $L$ lines each consisting of a string of length $W$, indicating the tiles of the map. Here ‘S’ denotes the start tile, ‘G’ denotes the goal tile, ‘W’ denotes a safe tile and ‘B’ denotes a lava tile.

-----Output-----
Output a line with the word “SUCCESS” if they both reach the goal at the same time, “GO FOR IT” if Elsa wins and “NO CHANCE” if the father would win. If neither Elsa nor her father is able to reach the goal, output “NO WAY”.

-----Limits-----
 - $1 \leq A \leq 1000$
 - $1 \leq F \leq 1000$
 - $1 \leq L \leq 1000$
 - $1 \leq W \leq 1000$
 - The number of ‘W’ tiles will be at most $1000$.
 - The map will only contain the characters ’S’, ’G’, ’W’ and ’B’ and there will only be one ’S’ character and one ’G’ character per map.

-----Examples-----
Sample Input:
2 3
4 4
WWWW
WSBB
WWWW
WBWG
Sample Output:
GO FOR IT
user: Stan Ford is a typical college graduate student, meaning that one of the most important things on his mind is where his next meal will be. Fortune has smiled on him as he’s been invited to a multi-course barbecue put on by some of the corporate sponsors of his research team, where each course lasts exactly one hour. Stan is a bit of an analytical type and has determined that his eating pattern over a set of consecutive hours is always very consistent. In the first hour, he can eat up to $m$ calories (where $m$ depends on factors such as stress, bio-rhythms, position of the planets, etc.), but that amount goes down by a factor of two-thirds each consecutive hour afterwards (always truncating in cases of fractions of a calorie). However, if he stops eating for one hour, the next hour he can eat at the same rate as he did before he stopped. So, for example, if $m=900$ and he ate for five consecutive hours, the most he could eat each of those hours would be $900$, $600$, $400$, $266$ and $177$ calories, respectively. If, however, he didn’t eat in the third hour, he could then eat $900$, $600$, $0$, $600$ and $400$ calories in each of those hours. Furthermore, if Stan can refrain from eating for two hours, then the hour after that he’s capable of eating $m$ calories again. In the example above, if Stan didn’t eat during the third and fourth hours, then he could consume $900$, $600$, $0$, $0$ and $900$ calories.

Stan is waiting to hear what will be served each hour of the barbecue as he realizes that the menu will determine when and how often he should refrain from eating. For example, if the barbecue lasts $5$ hours and the courses served each hour have calories $800$, $700$, $400$, $300$, $200$ then the best strategy when $m=900$ is to eat every hour for a total consumption of $800+600+400+266+177 = 2243$ calories. If however, the third course is reduced from $400$ calories to $40$ calories (some low-calorie celery dish), then the best strategy is to not eat during the third hour — this results in a total consumption of $1900$ calories.

The prospect of all this upcoming food has got Stan so frazzled he can’t think straight. Given the number of courses and the number of calories for each course, can you determine the maximum amount of calories Stan can eat?

-----Input-----
Input starts with a line containing two positive integers $n$ $m$ ($n \leq 100, m \leq 20000$) indicating the number of courses and the number of calories Stan can eat in the first hour, respectively. The next line contains $n$ positive integers indicating the number of calories for each course.

-----Output-----
Display the maximum number of calories Stan can consume.

-----Examples-----
Sample Input:
5 900
800 700 400 300 200
Sample Output:
2243
user: -----Input-----
The first line of input consists of two integers $N$ and $Q$, where $1 \le N \le 1000000$ is the number of elements in the base set and $0 \le Q \le 1000000$ is the number of operations. Then follow $Q$ lines, one per operation. There are two types of operations:
 - “= $a$ $b$” indicate that the sets containing $a$ and $b$ are joined
 - “? $a$ $b$” is a query asking whether $a$ and $b$ belong to the same set

In both cases, $a$ and $b$ are distinct integers between $0$ and $N-1$.

-----Output-----
For each query output a line containing “yes” if $a$ and $b$ are in the same set, and “no” otherwise.

-----Examples-----
Sample Input:
10 4
? 1 3
= 1 8
= 3 8
? 1 3
Sample Output:
no
yes
user: The Math department has challenged the Computer Science department at your University to solve a difficult puzzle in Discrete Mathematics. With the pride of your Computer Science department at stake, you must solve this puzzle!

In this puzzle, you are given a sequence of $n$ positive integers. The sequence must be partitioned into $k$ consecutive contiguous regions, with at least 1 integer in each region. After finding a partition, it is scored in a strange way. In each region, you must find the largest prime number that divides every number in that region. The Math department reminds you a prime number is an integer greater than 1 where its only divisors are 1 and itself. If you cannot find such a prime, your score for that region is 0. Your total score for the partition is the minimum over all regions.

Your task is to find the maximum possible score. The Math department will win if their score is better, so be sure to find the maximum each time!

-----Input-----
Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. Each input begins with a line with two space-separated integers $n$ ($1 \le n \le 20000$) and $k$ ($1 \le k \le \min (100,n)$), where $n$ is the number of positive integers in the original sequence, and $k$ is the number of regions in the partition. The next line contains $n$ space-separated integers $v$ ($1 \le v \le 1000000$). This is the sequence to be partitioned, in order.

-----Output-----
Output a single integer representing the maximum score possible partitioning the sequence of $n$ positive integers into $k$ regions.

-----Examples-----
Sample Input:
5 3
10 5 4 8 3
Sample Output:
2
user: Consider the following function $f(X)$, which takes a single positive integer as argument, and returns an integer.

function f(X): iterations := 0 while X is not 1: if X is even: divide X by 2 else: add 1 to X add 1 to iterations return iterations

It can be shown that for any positive integer $X$, this function terminates. Given an interval $[L, R]$, compute the sum\[ S = f(L) + f(L+1) + \cdots + f(R-1) + f(R)\enspace . \]

-----Input-----
The first and only line of input contains two integers $L$ and $R$ ($1 \leq L \leq R \leq 10^{18}$).

-----Output-----
Output the result $S$ modulo the prime $10^9+7$.

-----Examples-----
Sample Input:
1 127
Sample Output:
1083
user: In the TV quiz Monstermind, a contestant chooses a topic and is then asked questions about it during a fixed period of time. The contestant earns one point for each correct answer. When the time runs out, the contestant must be silent.

Teresa has figured out such a niche topic that she knows all possible questions that may be asked about it, as well as all the answers. Since the competition is fierce, she has decided to sometimes answer a question before the host finishes reading it. The host picks each question uniformly at random from the pool of possible questions, and each question may be asked multiple times. When reading a question, the host reads at a pace of one word per second.

Teresa can interrupt the host mid-question—between words, or even before hearing the first word—but not mid-word—that would be extremely impolite. Answering also takes one second, and the host will start reading another question immediately after an answer—unless Teresa interrupts again.

She wrote a program to help her choose the best moment to answer, and now there is only one question left for you. How many points does she expect to score?

For example, in the first sample test case the answer is completely determined after hearing one word, so it is optimal to answer after hearing it, and Teresa answers 2 questions correctly in 4 seconds. In the second sample test case, if the first word is What, then it takes too much time to wait for the question to finish. Therefore Teresa says Now! 4 times and expects to get $1/3$ of the answers right.

-----Input-----
The first line contains two integers $t$ and $n$ ($1 \leq t \leq 100$, $1 \leq n \leq 100\ 000$), the duration of the quiz and the number of questions. Each of the following $n$ lines contains a question, which is a space-separated list of words terminated by a question mark; and an answer, which is a single word.

Each word is a sequence of non-space ASCII printable characters, between the ASCII values of ‘!’ and ‘$\sim $’. Only the last word of a question has a question mark (‘?’). You can assume that no question is a prefix of another and that punctuation marks are part of a word. Words spelled with different upper/lower case are assumed to be different.

It is guaranteed that the total number of word characters is at most $100\ 000$.

-----Output-----
Output the expected score of an optimal strategy. Answers within a relative or absolute error of $10^{-6}$ will be accepted.

-----Examples-----
Sample Input:
4 4
How much is 6 times 9? 42
How much is 9 times 6? 42
Is there intelligent life on Earth? Probably
What is the air speed velocity of an unladen swallow? African?
Sample Output:
2.0000000000