meetforever/GRPO_CL huggingface dataset:
user: You have been invited to host a famous radio show to tell your fascinating life story and play some of your favorite songs. However, choosing which songs to play is turning out to be very tricky; there are just way too many good songs and you only have enough time to play a measly nine songs! 

In order to give the show a sense of continuity, you have decided that consecutive songs you play should have some detail in common. For instance, if you start by playing Björk’s song “Pagan Poetry”, you could continue with next playing matmos’ track “Enigma Machine for Alan Turing” since matmos contributed to Björk’s Vespertine album (on which Pagan Poetry appears). Continuing, you might play a part of Prokofiev’s “Петя и волк”, as it was written in 1936, the same year as Alan Turing’s seminal paper on undecidability of the Halting Problem, and so on. The ordering of the songs is important, so just because you could play song X after song Y it will not necessarily be the case that you can play song Y after song X. At the same time as achieving this sense of continuity, you also want the playlist to have a bit of variation, so all nine songs must be by different artists.

You have narrowed things down to a bunch of your favorite songs, but finding a list of nine songs with a common thread seems tricky. Maybe you could use your programming skills to find a good playlist?

-----Input-----
The first line of input consists of an integer $n$ ($9 \le n \le 100$), the number of songs. Then follow $n$ lines. Each line describes a song, starting with the name of the artist (as a string of ‘a’-‘z’ of at most $15$ characters), followed by an integer $t$ ($1 \le t \le 40$), the number of songs that can be played directly after this song. Then follows (on the same line) $t$ distinct integers $s_1, \ldots , s_ t$, each between $1$ and $n$, giving the numbers of the songs that can be played after the current song. The songs are numbered from $1$ to $n$, with song number $1$ being described on the first line, and so on.

-----Output-----
If there is a playlist of nine songs satisfying the requirements, output a list of nine integers giving the numbers of the songs (according to the same numbering as in the input), in the order they should be played. Otherwise, output a single line containing the word “fail”. If there is more than one valid playlist, any one of them will be accepted.

-----Examples-----
Sample Input 1:
10
a 2 10 3
b 1 6
c 2 1 5
d 1 9
e 1 4
f 1 2
g 2 6 8
h 0
i 1 3
j 1 7
Sample Output 1:
5 4 9 3 1 10 7 6 2

Sample Input 2:
10
a 2 10 3
a 1 6
c 2 1 5
d 1 9
e 1 4
f 1 2
g 2 6 8
h 0
i 1 3
j 1 7
Sample Output 2:
fail
user: Arghs! Yet again, all the clocks in Petra’s home show the wrong time due to a power outage that occurred while she was sleeping. This means she has to spend her day resetting all the clocks to the correct time. Now, you might not consider this a big deal. After all, how many clocks does any single household really have? Well, Petra just so happens to be a collector of clocks. She literally has hundreds of clocks – and that is just in her bedroom! Thus, it is understandable that she does not look forward to all this resetting. 

You, as her friend, would prefer if she did not need to spend her entire day resetting all her clocks. Especially since this means she would not have any time to play with you! If only you could construct some automated way of entering the correct time into all the clocks, perhaps through some kind of computer code...

A-ha, of course! You can write a program to determine how to set the correct time as quickly as possible!

Each clock has a display of $4$ digits: two are used to display the hour (between 00 and 23), and two are used to display the minute (between 00 and 59). The time can be changed by selecting a digit and either decreasing or increasing by $1$. Decreasing a digit that is $0$, it is turned into $9$, and increasing a digit $9$ turns it into $0$. However, the clock can not display invalid times. This means that at any given time, the hour must be between 00 and 23 and the minute between 00 and 59.

Write a program that, given the original time of a clock and the current time, determines how to set the clock correctly.

-----Input-----
The input consists:
 - one line with the time that the clock is currently set to.
 - one line with the current time.

Each time has the format hh:mm, where hh is a two-digit number between 00 and 23, and mm is a two-digit number between 00 and 59.

-----Output-----
The first line contains the number of different times seen on the clock when setting it correctly. Then for each time output it on the same format as above hh:mm on a separate line. Include both the original time and the final time.

-----Examples-----
Sample Input 1:
00:00
01:01
Sample Output 1:
3
00:00
01:00
01:01

Sample Input 2:
00:08
00:00
Sample Output 2:
3
00:08
00:09
00:00
user: Balanced closed bracket or parenthesis statements are ones where each opening bracket is matched with a closed bracket later in the string.

Notice how each closed parenthesis matches to the most recent unmatched open parenthesis.

Define an alternative bracket notation as follows: each bracket pair corresponds to a header in the form of “start,end:” where start and end are indices of the new string itself! The index start is the index of the character immediately after the ‘:’, and end is the index past the last header corresponding to the last bracket pair contained in this bracket pair. By taking a substring(start, end) of the new notation, you get an alternative bracket sequence describing all of the pairs of brackets contained by the brackets corresponding to the “start,end:”! Since an empty pair of brackets has nothing inside, in their header, start and end will be the same.

Each index takes up as many characters in the string as they do when they are base $10$ numbers. (For example, the index $42$ will take up $2$ characters). The indices in the new string start from $0$. All of the indices found in the alternative bracket notation string are absolute indices from the beginning of the new string.

Consider this parenthetical statement: (())

Here is it, in our new, alternate bracket notation: 4,8:8,8:

In this example, there are two sets of matching parenthesis, the outer one and the inner one. The outer one appears before the inner one, since the start bracket appears first. So, the header for the outer brackets will appear before the header for the inner bracket. The header 4,8: represents the outer bracket, while the header 8,8: represents the inner bracket. The substring from the $4$th character to $7$th character is 8,8:, which represents what is contained inside the outer bracket. Note that 5,11:11,11: could also be a legitimate alternate notation, but we want the shortest one, which is why 4,8:8,8: is the correct answer.

-----Input-----
Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. The input will consist of a single line, containing a string $s$, which consists only of open and closed parentheses. The string $s$ will be between $2$ and $4000$ characters long. There will be no spaces. The string $s$ is guaranteed to be balanced.

-----Output-----
Output the string $s$ in our new alternative bracket notation. If there’s more than one way to represent $s$ in the new notation, choose the shortest representation, which will be unique.

-----Examples-----
Sample Input 1:
(())
Sample Output 1:
4,8:8,8:

Sample Input 2:
()
Sample Output 2:
4,4:
user: The European Space Agency has $N$ telescopes observing distant planets. They have classified $M$ different types of events. They noticed that every day on each planet there is exactly one type of event. They measure events in days because they discovered each event lasts at least one day, and at most 365 days. Events last only complete numbers of days, they never last a fractional part of a day. Each event of the same type lasts exactly the same number of days every time it occurs, regardless of the planet it occurs on.

After many years of observation they want to analyze data. The telescopes logged all observations, but unfortunately they forgot to write down the year the observations took place! Each telescope entry consists of start date, end date and the number of events observed of each type. Given all observations on all the planets, calculate the duration of each type of event. Note that the telescopes are super precise and start working exactly when the event starts and end when an event ends, not necessarily the same one.

Note: for this task, each year has exactly 365 days.

-----Input-----
The first line contains $N$ and $M$ ($1 \le N, M \le 200$) - the number of telescopes and the number of event types. The next $N$ lines each contains $M + 4$ numbers each:

$D_1\text { }M_1\text { }D_2\text { }M_2\text { }F_1\text { }F_2\text { }...\text { }F_ M$

where $D_1, M_1$ ($01 \le D \le 31, 01 \le M \le 12$) is the start date, $D_2, M_2$ is the end date and $F_ i$ ($0 \le F_ i \le 200$) is the number of times event $I$ was observed.

Note that the days $D_ i$ and months $M_ i$ will always be zero-padded to exactly 2 characters.

-----Output-----
One line containing $M$ numbers, the durations of the event types. If more than one solution exists, output any one. If no solution exists, output “-1” (without quotes).

-----Examples-----
Sample Input 1:
1 1
26 02 03 03 1
Sample Output 1:
5

Sample Input 2:
1 1
26 02 03 03 2
Sample Output 2:
185
user: Note that this is a harder version of problem dance. The change to the previous version is marked in bold.

Marek loves dancing and he has danced a lot in the last couple of years. He has actually danced so much that he became too good in all of the traditional dances like swing, salsa, ballroom and hip-hop and now all partners he dances with can not keep up with him. Therefore he started to invent his own dances and even tries to convince other people to dance these new dances with him.

Marek got really excited when he heard about the coming wedding of his best friend Miroslav. For a whole month he worked on a special dance for the wedding. The dance was performed by $N$ people and there were $N$ marks on the floor. There was an arrow from each mark to another mark and every mark had exactly one incoming arrow. Marek did not want anyone to stand on one place the whole time, so no arrow pointed from a mark back to the same mark.

At the wedding, every person first picked a mark on the floor and no 2 persons picked the same one. Then Marek played some music and every 10 seconds there was a loud signal when all dancers had to move along the arrow on the floor to another mark. The placement of the marks was such that everybody could follow the arrow to the next mark in 10 seconds without any trouble.

A year has passed since Miroslav’s wedding and another wedding is coming up. Marek would like to do a similar dance at this wedding as well. He lost all the drawings he had, but luckily he found two photos from exactly when the dance started and when it ended. Marek also remembers that the signal was triggered $K$ times during the time the song was played, so people moved $K$ times along the arrows.

Given the two photos, can you help Marek reconstruct the arrows on the floor so that each arrow connects two different marks? On the two photos it can be seen for every person to which position he or she moved. Marek therefore numbered the people in the first photo from $1$ to $N$ and then wrote the number of the person whose place they took in the second photo.

Marek’s time is running out, so he is interested in any placement of arrows that could produce the two photos.

-----Input-----
The first line of the input contains two integers $N$ and $K$, $2 \le N \le 10000, 1\le K \le 10^9$. The second line of the input contains $N$ space separated integers $a_1, \dots , a_ N$, denoting that dancer number $i$ ended at the place of dancer number $a_ i$. You may assume that $1 \le a_ i \le N$ for all $i$ and every number between $1$ and $N$ inclusive appears exactly once in the sequence.

-----Output-----
If it is impossible to find a placement of arrows such that the dance performed $K$ times would produce the two photos, print “Impossible”. Otherwise print $N$ numbers on a line, the $i$-th number denoting to which person the arrow leads from person number $i$. Note that the $i$-th number cannot be $i$, because then the person would not move the whole time. If there are more solutions, you can print any one.

-----Examples-----
Sample Input 1:
6 2
3 4 5 6 1 2
Sample Output 1:
5 6 1 2 3 4 

Sample Input 2:
4 2
3 4 1 2
Sample Output 2:
2 3 4 1
user: You are given a positive integer $n$ and asked to make it larger by swapping pairs of its digits. For each swap, you can choose two digits at different positions and exchange their positions, as long as the swap does not result in a leading zero. What is the largest number you can get after performing exactly $k$ swaps?

-----Input-----
The input has a single line with two integers $n$ ($100 \leq n < 10^{18}$) and $k$ ($1 \leq k \leq 18$).

-----Output-----
Output the largest number you can get after exactly $k$ swaps.

-----Examples-----
Sample Input 1:
1374 2
Sample Output 1:
7413

Sample Input 2:
210 1
Sample Output 2:
201
user: You are operating a taxi company in the Land of Bytes, which is an interesting city. First, all roads in the city either along the north-south direction or along the east-west direction. Second, it’s an extremely large city such that the sizes of blocks between different roads are negligible. Therefore, each position in this city can be represented by coordinates $(x, y)$ of real values.

The taxi drivers always takes the shortest path between the pick-up and drop-off points, following streets. Your company only operates the taxis within the central business district (CBD), which is a convex polygon of $n$ points.

Assuming the pick-up and drop-off points from the passengers are chosen, uniformly at random, from inside the CBD, what is the expected distance that a taxi will travel? Assume the taxi travel distance between any points $(x, y)$ and $(x_1, y_1)$ is always $|x-x_1|+|y-y_1|$.

-----Input-----
The first line contains an integer $n$ ($3 \le n \le 100000$).

Following this will be $n$ lines, each with two integer values values ($x, y$) representing the points on the border of CBD, where $|x|,|y| < 10^9$. The points are presented in a clockwise order and there will be no three points on the same line.

-----Output-----
The output is a single line containing one number, the expected distance expressed with a relative or absolute error less than $10^{-6}$.

-----Examples-----
Sample Input 1:
4
0 0
0 1
1 1
1 0
Sample Output 1:
0.666666666666667

Sample Input 2:
3
0 0
1 1
2 0
Sample Output 2:
0.733333333333333
user: Providing wireless network coverage for a large office can be tricky. In this problem you are asked to set up wireless network coverage for an entire office floor plan. The floor plan can be viewed as an $N\times M$ grid. Each grid cell represents a single office. Each pair of adjacent offices (cells that share a side) are connected by a corridor. You may install routers in some of the offices. Each installed router provides wireless network for the (at most four) corridors that are incident to the office where the router is located. Installing routers at different offices may have different costs.

However, some issues arise. If neither of the two offices incident to a corridor has a router, the corridor would have weak signal. If both of the two offices incident to a corridor have a router, the corridor would have conflicting signals that would cause both routers to be inaccessible from the corridor. (Unfortunately the routers available are pretty old models that do not collaborate very well.) Consequently, for every corridor that has either weak or conflicting signal, you must additionally install a cellular hub, which provides separate wireless service (that uses cellular network and is independent of the routers). Each cellular hub is sold for $K$ dollars.

Find the minimum total cost to set up a wireless network that covers every corridor.

-----Input-----
The first line of the input has three integers $N$, $M$ ($2 \leq N, M \leq 40$), and $K$ ($0\leq K \leq 200$). The next $N$ lines contains $M$ non-negative integers each. The $j$-th integer on the $i$-th line is the cost (in dollars) of installing a router in the office at the $i$-th row, $j$-th column of the floor plan. All costs are no larger than $200$.

-----Output-----
Output the minimum total cost (in dollars) to provide a wireless network that covers every corridor.

-----Examples-----
Sample Input 1:
2 3 4
10 1 3
0 1 20
Sample Output 1:
9

Sample Input 2:
2 3 100
10 1 10
10 1 10
Sample Output 2:
21
user: KenKen is a popular logic puzzle developed in Japan in 2004. It consists of an $n \times n$ grid divided up into various non-overlapping sections, where each section is labeled with an integer target value and an arithmetic operator. The object is to fill in the entire grid with the numbers in the range 1 to $n$ such that
 - no number appears more than once in any row or column
 - in each section you must be able to reach the section’s target using the numbers in the section and the section’s arithmetic operator

For this problem we are only interested in single sections of a KenKen puzzle, not the entire puzzle. Two examples of sections from an $8 \times 8$ KenKen puzzle are shown below along with some of their possible assignments of digits.

 Figure C.1 

Note that while sections labeled with a subtraction or division operator can consist of only two grid squares, those labeled with addition or multiplication can have any number. Also note that in a $9 \times 9$ puzzle the first example would have two more solutions, each involving the numbers $9$ and $2$. Finally note that in the first solution of the second section you could not swap the $1$ and $4$ in the first row, since that would result in two $1$’s in the same column.

You may be wondering: for a given size KenKen puzzle and a given section in the puzzle, how many valid ways are there to fill in the section? Well, stop wondering and start programming!



-----Input-----
The input will start with a single line of the form $n$ $m$ $t$ $op$, where $n$ is the size of the KenKen puzzle containing the section to be described, $m$ is the number of grid squares in the section, $t$ is the target value and $op$ is either ‘+’, ‘-’, ‘*’ or ‘/’ indicating the arithmetic operator to use for the section.

Next will follow $m$ grid locations of the form $r$ $c$, indicating the row and column number of the grid square. These grid square locations will take up one or more lines.

All grid squares in a given section will be connected so that you can move from any one square in the section to any other by crossing shared lines between grid squares.

The values of $n$, $m$ and $t$ will satisfy $4\leq n\leq 9$, $2 \leq m \leq 10$, $0 < t \le 3 \cdot 10^8$ and $1 \leq r,c \leq n$.

-----Output-----
Output the number of valid ways in which the section could be filled in for a KenKen puzzle of the given size.

-----Examples-----
Sample Input 1:
8 2 7 -
1 1 1 2
Sample Output 1:
2

Sample Input 2:
9 2 7 -
1 1 1 2
Sample Output 2:
4
user: A road network in a country consists of $N$ cities and $M$ one-way roads. The cities are numbered $1$ through $N$. For each road we know the origin and destination cities, as well as its length.

We say that the road $F$ is a continuation of road $E$ if the destination city of road $E$ is the same as the origin city of road $F$. A path from city $A$ to city $B$ is a sequence of road such that origin of the first road is city $A$, each other road is a continuation of the one before it, and the destination of the last road is city $B$. The length of the path is the sum of lengths of all roads in it.

A path from $A$ to $B$ is a shortest path if there is no other path from $A$ to $B$ that is shorter in length.

Your task is to, for each road, output how many different shortest paths contain that road, modulo $1000000007$.

-----Input-----
The first line contains two integers $N$ and $M$ $(1 \le N \le 1500, 1 \le M \le 5000)$, the number of cities and roads.

Each of the following $M$ lines contains three positive integers $O$, $D$ and $L$. These represent a one-way road from city $O$ to city $D$ of length $L$. The numbers $O$ and $D$ will be different and $L$ will be at most $10000$.

-----Output-----
Output $M$ integers each on its own line – for each road, the number of different shortest paths containing it, modulo $1000000007$. The order of these numbers should match the order of roads in the input.

-----Examples-----
Sample Input 1:
4 3
1 2 5
2 3 5
3 4 5
Sample Output 1:
3
4
3

Sample Input 2:
4 4
1 2 5
2 3 5
3 4 5
1 4 8
Sample Output 2:
2
3
2
1
user: Little Mirko spends his free time painting. For this hobby, he likes to use brushes and a palette containing $K$ colors overall. His friend Slavko decided to use Mirko’s talent and gave him his new coloring book for Mirko to color. The coloring book contains $N$ images numbered $1, 2, \ldots , N$.

Mirko has decided to paint each image in exactly one color of the possible $K$ colors from his palette. However, he really likes colorful things. He chose $N$ numbers $f_ i$ and decided to paint the image numbered $i$ differently than the images numbered $f_ i$, except when $f_ i = i$. If $f_ i = i$, that means he can paint the image numbered $f_ i$ whichever color he likes, as long as all other conditions have been met.

Mirko wants to know the number of possible ways to color Slavko’s coloring book and he desperately needs your help! Calculate the number of possible ways to color the book. Given the fact that the output can be very large, print the answer modulo $1000000007$.

-----Input-----
The first line of input contains positive integers $N$, $K$ ($1 \leq N, K \leq 1000000$). The following line contains N numbers $f_ i$ ($1 \leq f_ i \leq N$), as stated in the text.

-----Output-----
The first and only line must contain the number of possible ways to color Slavko’s book.

-----Examples-----
Sample Input 1:
2 3
2 1
Sample Output 1:
6

Sample Input 2:
3 4
2 3 1
Sample Output 2:
24
user: The latest hit song Chair Hopping contains instructions for a group dance. To perform the dance, $n$ performers numbered from $1$ to $n$ and $n$ chairs numbered from $1$ to $n$ are required. Initially, performer $i$ is seated in chair $i$.

When a single hop is performed, the performer currently seated in chair $i$ moves to chair $s_ i$. The values of $s_ i$ are distinct, ensuring that each chair will be filled by exactly one performer after the hop is completed.

Exactly two hops have been completed and now performer $i$ is sitting in chair $t_ i$. Observing that, you wonder in how many ways the values of $s_ i$ can be chosen. The answer can be large. Output it modulo $10^9 + 7$.

-----Input-----
The first line of the input contains the integer $n$ ($1 \leq n \leq 10^5$). The second line of the input contains $n$ distinct integers $t_1, t_2, \dots t_ n$ ($1 \leq t_ i \leq n$).

-----Output-----
Output the number of ways in which the values of $s_ i$ can be chosen, modulo $10^9 + 7$.

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

Sample Input 2:
5
3 4 5 1 2
Sample Output 2:
1