meetforever/GRPO_CL huggingface dataset:
user: You think you can code?

 This problem will test you on various basic programming techniques.

 You are given two integers $N$ and $t$; and then an array $A$ of $N$ integers ($0$-based indexing).

 Based on the value of $t$, you will perform an action on $A$.

$t$

Action Needed

$1$

Print “Yes” if there are two integers $x \in A$ and $y \in A$ such that $x \neq y$ and $x+y = 7777$, 

or “No” otherwise (without the quotes)

$2$

Print “Unique” if all integers in $A$ are different; 

or print “Contains duplicate” otherwise (without the quotes)

$3$

Find and print the integer that appears $> \frac{N}{2}$ times in $A$; 

or print $-1$ if such integer cannot be found

$4$

Find and print the median integer of $A$ if $N$ is odd; 

or print both median integers of $A$ if $N$ is even (separate them with a single space)

$5$

Print integers in $A$ that fall between a range [$100 \ldots 999$] in sorted order; 

(print a single space between two integers)

-----Input-----
The first line of the input contains an integer $N$ and $t$ ($3 \leq N \leq 200000$; $1 \leq t \leq 5$).

 The second line of the input contains $N$ non-negative $32$-bit signed integers.

-----Output-----
For each test case, output the required answer based on the value of $t$.

-----Scoring-----
There are $20$ hidden test cases that test various requirements of this problem.

 All $20$ test cases will be tested.

 Each hidden test case worth $5$ points (the $5$ sample test cases below worth $0$ point).

-----Examples-----
Sample Input 1:
7 1
1 7770 3 4 5 6 7
Sample Output 1:
Yes

Sample Input 2:
7 2
1 2 3 4 5 6 7
Sample Output 2:
Unique

Sample Input 3:
7 3
1 1 1 1 2 2 2
Sample Output 3:
1

Sample Input 4:
8 4
8 1 4 3 6 7 5 2
Sample Output 4:
4 5
user: It is finally Bobby’s birthday, and all of his Acquaintances, Buddies and Colleagues have gathered for a board game night. They are going to play a board game which is played in up to three big teams. Bobby decided to split his guests into groups based on how well he knows them: the Acquaintances on team $A$, the Buddies on team $B$, and the Colleagues on team $C$.

While Bobby was busy explaining the rules to everyone, all his guests already took seats around his large, circular living room table. However, for the game it is crucial that all people sitting on a team are sitting next to each other. Otherwise, members of other teams could easily eavesdrop on their planning, ruining the game. So some people may need to change seats to avoid this from happening.

Bobby wants to start playing the game as soon as possible, so he wants people to switch seats as efficiently as possible. Given the current arrangement around the circular table, can you figure out the minimal number of people that must switch seats so that the teams are lined up correctly?

-----Input-----
 - The first line of the input contains the integer $n$, where $1 \leq n \leq 10^5$ is the number of players (as well as seats).
 - The second line contains a string of length $n$, consisting only of the characters in ABC. This indicates the teams of the people sitting around the table in order.

-----Output-----
Print a single integer: the minimal number of people you have to ask to move seats to make sure the teams sit together.

-----Examples-----
Sample Input 1:
5
ABABC
Sample Output 1:
2

Sample Input 2:
12
ABCABCABCABC
Sample Output 2:
6

Sample Input 3:
4
ACBA
Sample Output 3:
0

Sample Input 4:
6
BABABA
Sample Output 4:
2
user: You are attending the International Construction by Preschoolers Contest. Unfortunately, you are too old to participate, but you still enjoy watching the competition.

In between rounds, you are walking around the contest area when you see a toddler, one of the contestants, playing with her blocks. Annoyed that she is having all the fun, you decide to challenge her to a game.

You set up two stacks of blocks of a certain height. Then, you and the toddler take turns removing some number of blocks from the stack which contains the largest number of blocks (if both stacks have the same number of blocks, the current player can choose either stack to remove blocks from). The number of blocks removed must be a positive multiple of the number of blocks in the smaller stack. For instance, if there is a stack with $5$ blocks, and one with $23$ blocks, then the current player can remove $5$, $10$, $15$ or $20$ blocks from the stack of $23$ blocks. The player who empties one of the stacks wins the game.

You have graciously decided to take the first move, but then a worry strikes you – might this devious preschooler still be able to beat you?

-----Input-----
One line with two integers $N$ and $M$, satisfying $1 \leq N, M\leq 10^{18}$, the initial sizes of the two stacks of blocks.

-----Output-----
Output a single line containing a single word: the word “win” if you are guaranteed to win if you play correctly, and the word “lose” if your opponent can force you to lose.

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

Sample Input 2:
3 3
Sample Output 2:
win

Sample Input 3:
5 2
Sample Output 3:
win

Sample Input 4:
5 3
Sample Output 4:
win
user: Given an orthogonal maze rotated $45$ degrees and drawn with forward and backward slash characters (see below), determine the minimum number of walls that need to be removed to ensure it is possible to escape outside of the maze from every region of the (possibly disconnected) maze.

/\
\/

This maze has only a single region fully enclosed. Removing any wall connects it to the outside.

/\..
\.\.
.\/\
..\/

This maze has two enclosed areas. Two walls need to be removed to connect all regions to the outside.

-----Input-----
The first line has two numbers, $R$ and $C$, giving the number of rows and columns in the maze’s input description. Following this are $R$ lines each with $C$ characters, consisting only of the characters ‘/’, ‘\’, and ‘.’. Both $R$ and $C$ are in the range $1\ldots 1000$.

Define an odd (even) square as one where the sum of the $x$ and $y$ coordinates is odd (even). Either all forward slashes are in the odd squares and all backslashes in the even squares, or vice versa.

-----Output-----
Output on a single line an integer indicating how many walls need to be removed so escape is possible from every region in the maze.

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

Sample Input 2:
4 4
/\..
\.\.
.\/\
..\/
Sample Output 2:
2

Sample Input 3:
2 2
\/
/\
Sample Output 3:
0
user: Farmer Laura has a barn. In her barn, she has two cows, Monica and Lydia. Monica and Lydia love food, and they are quite lazy. For most of the day they chill out in the barn, waiting for Laura to come serve them a nice meal. Farmer Laura is always very precise about when to serve them food, so Monica and Lydia know exactly when to expect food, the same time every day.

This might sound surprising to you but there’s a problem. Farmer Laura needs your help. She will be replacing some planks in the floor of the barn, which means that the cows have to be moved temporarily from their favorite spots. Since the cows are infinitely lazy, they refuse to walk themselves. Farmer Laura has rented an excellent tool to resolve this issue – a cow crane, designed and crafted specifically for the cow’s comfort.

We visualize the barn as a one-dimensional line. The cow crane starts at time $t = 0$ at position $x = 0$, and it can move one distance unit per second. The crane can only carry one cow at a time, but it may pick up and drop off a cow as many times as necessary. Monica’s current location is at $x = m$, and Lydia is located at $x = l$. Monica will be moved to the temporary location at $x = M$ and Lydia to $x = L$. Monica and Lydia always have their daily meal $t_ m$ and $t_ l$ seconds into the day, so the cows had better be in their respective temporary locations exactly by these times. You may assume that it takes no time for the crane to pick up or drop off a cow and that the two cows can be at the same position at the same time.

-----Task-----
Farmer Laura would like to know if she can move the cows so that both of them are in place at their temporary location no later than their daily meal occurs.

-----Input-----
Input consists of three lines. The first line consists of two integers $m$ and $l$, the current positions of the cows. The second line consists of two integers $M$ and $L$, the new positions of the cows. The third line consists of two integers $t_ m$ and $t_ l$, the time at which the two cows will be served their daily meal. It is guaranteed that $-10^8 \leq m, l, M, L \leq 10^8$ and $1 \leq t_ m, t_ l \leq 10^8$. It is also guaranteed that both cows will actually move, i.e., $m \not= M$ and $l \not= L$.

-----Output-----
Output should consist of a single word. Print “possible” if it is possible to move both cows before they are served their daily meal. Otherwise, print “impossible”.

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

Sample Input 2:
-1 1
-2 2
5 5
Sample Output 2:
impossible

Sample Input 3:
-1 1
1 -1
3 5
Sample Output 3:
possible
user: Robot Turtles is one of Theta’s favorite games. In this game, kindergarteners learn how to “code” by creating programs that move a turtle from a starting field to a diamond. Robot Turtles is reportedly the most successful game funded by the Kickstarter incubator.

Players must develop a program consisting of “instructions” that brings a turtle from a starting location to a goal (a diamond). An adult will then “execute” this program by moving the turtle based on the given instructions.

Robot Turtles is played on an $8 \times 8$ board. There is one turtle (marked with the letter T), which always starts out at the bottom-left field, facing right. The board contains empty squares (marked as .), castles made out of rock (C), and castles made out of ice (I). The diamond is marked with a D. The turtle may move only onto empty squares and the square on which the diamond is located.

A turtle program contains $4$ kinds of instructions, marked by a single letter.
 - F The turtle moves one field forward in the direction it is facing. If the turtle faces a castle or the border of the board, a program error occurs.
 - R The turtle turns $90$ degrees to the right (the turtle will just turn and stay on the same field).
 - L The turtle turns $90$ degrees to the left (the turtle will just turn and stay on the same field).
 - X The turtle fires a laser in the direction it is facing. If the square it is facing contains an ice castle, the ice castle will melt and the square will turn into an empty square. Otherwise, a program error occurs. The turtle will not move or change direction. It is a program error to fire the laser at empty squares, rock castles or outside the board.

-----Input-----
The input consists of $8$ lines, which represents the board, with each line representing one row. The turtle will always start out at the bottom-left. There will be exactly $1$ diamond. There will be no more than $10$ ice castles.

-----Output-----
Output the shortest valid turtle program whose execution (without program error) brings the turtle from the starting location to the diamond! If there are multiple such programs of equal length, you may output any of them!

Output no solution if it is not possible for the turtle to reach the diamond!

-----Examples-----
Sample Input 1:
........
........
........
...CC...
..C.DC..
.C..C...
C.IC....
T.C.....
Sample Output 1:
FLFRXFLFRFLFRF

Sample Input 2:
........
........
........
...CC...
..CIDC..
.CI.C...
C.IC....
T.C.....
Sample Output 2:
FLFRXFLXFRFLXFRF

Sample Input 3:
........
........
........
...CCD..
..C..C..
.C..I...
C.IC....
T.C.....
Sample Output 3:
FLFRXFLFRFXFFFLFFLF
user: You are the founder of the Bruce Arden Programming Collective, which is a tutoring programme that matches experienced programmers with newbies to teach them. You have $N$ students and $N$ tutors, but now you have to match them up. Since the students will have to travel to their tutors’ houses from their own (or vice versa) you decide to do your matching based on travel distance.

Minimising overall distance doesn’t seem fair; it might happen that one student has to travel a huge distance while all the other students get a tutor very close by, even though the tutors could have been split up so that each gets a tutor that is at least somewhat close.

Thus, you opt to minimise the distance travelled by the student who is worst off; one pairing of students to tutors is better than another if the student who has to travel farthest in the first pairing has to travel less far than the student who has to travel farthest in the second pairing.

Because the students live in a city, the distance that a student needs to travel is not the literal distance between them and their tutor. Instead, the distance between points $(X,Y)$ and $(X’,Y’)$ in the city is\[ |X - X’| + |Y - Y’|. \]

-----Input-----
The first line of the input contains an integer $N$, with $1 \leq N \leq 100$, the number of students and the number of tutors to pair up.

Then, there are $N$ lines, each with two integers with absolute value at most $10^8$, which give the locations of the $N$ students.

These are followed by $N$ lines, each with two integers with absolute value at most $10^8$, which give the locations of the $N$ tutors.

Note that it is possible for students and/or tutors to have identical locations (they may share a house).

-----Output-----
Output a single line containing a single integer $K$, where $K$ is the least integer such that there exists a pairing of students to tutors so that no pair has distance greater than $K$ between them.

-----Examples-----
Sample Input 1:
2
0 0
0 3
0 2
0 5
Sample Output 1:
2

Sample Input 2:
4
0 1
0 2
0 3
0 4
1 0
1 1
1 2
1 3
Sample Output 2:
2

Sample Input 3:
3
0 5
5 2
4 5
3 3
5 2
5 2
Sample Output 3:
5
user: One of the most difficult things about going on a holiday is making sure your luggage does not exceed the maximum weight. You, chairman of the Backpacker’s Association for Packing Carry-ons, are faced with exactly this problem. You are going on a lovely holiday with one of your friends, but now most of your time is spent in frustration while trying to pack your backpack. In order to optimize this process, you and your friend have independently set upon trying to find better ways to pack.

After some time you have a serious breakthrough! Somehow you managed to solve the Knapsack problem in polynomial time, defying expectations everywhere. You are not interested in any theoretical applications, so you immediately return to your friend’s apartment in order to now quickly pack your backpack optimally.

When you arrive there, you find that your friend has set upon her own solution, namely to enumerate all possible packings. This means that all items you possibly wanted to bring are scattered across the entire apartment, and it would take a really long time to get all the items back together.

Luckily you can use the work your friend has done. For every possible subset of items that you can possibly bring, she has written down the total weight of these items. Alas, she did not write down what items were part of this total, so you do not know what items contributed to each total weight. If the original weights of the items formed a collection $(a_1,\dotsc ,a_ n)$ of non-negative integers, then your friend has written down the multiset\[ S\big ((a_1,\dotsc ,a_ n)\big ) := \left\{ \sum _{i \in I} a_ i \; \middle |\; I \subseteq \{ 1, \dots , n\} \right\} . \]

For example, if your friend had two items, and the weights of those two items are $2, 3$, then your friend has written down
 - $0$, corresponding to the empty set $\{ \} $;
 - $2$, corresponding to the subset $\{ 2\} $;
 - $3$, corresponding to the subset $\{ 3\} $;
 - $5$, corresponding to the subset $\{ 2, 3\} $.

You want to reconstruct the weights of all the individual items so you can start using your Knapsack algorithm. It might have happened that your friend made a mistake in adding all these weights, so it might happen that her list is not consistent.

-----Input-----
 - One line containing a single integer $1\leq n\leq 18$ the number of items.
 - $2^n$ lines each containing a single integer $0\leq w\leq 2^{28}$, the combined weight of a subset of the items. Every subset occurs exactly once.

-----Output-----
Output non-negative integers $a_1, \dotsc , a_ n$ on $n$ lines in non-decreasing order such that $S\big ((a_1,\dotsc ,a_ n)\big )=\{ b_1,\dotsc ,b_{2^n}\} $, provided that such integers exist. Otherwise, output a single line containing impossible.

-----Examples-----
Sample Input 1:
1
0
5
Sample Output 1:
5

Sample Input 2:
3
7
5
2
4
1
6
3
0
Sample Output 2:
1
2
4

Sample Input 3:
2
0
1
2
4
Sample Output 3:
impossible
user: Jacob is playing a very odd solo card game called StopCard. In this game, the deck consists of $n$ cards where every card has one unique integer written on one side of it. The deck is shuffled randomly before the game is played. During each turn of the game, Jacob can choose to either take a card off the top of the deck and read that value, or not take a card off the deck and end the game. His final score for the game is the value of the last card taken from the deck. The deck will always have at least one card, and the first turn of the game must always be to draw the top card of the deck.

Jacob has a basic understanding of optimal stopping theory, so he devises a plan to play the game somewhat effectively. His plan is to keep drawing cards for a predetermined number ($c$) of times, then to keep going until he sees a card that is larger than all the cards he previously saw, then to stop. His score will be the value written on that card. If he never sees a larger value on a card than the first cards he skipped, he would continue drawing until the deck runs out and would be left with a score equal to the number on the last card in the deck.

What is Jacob’s expected score under this strategy?

-----Input-----
The input consists of a single test case. The first line contains two integers $n$ and $c$ denoting the number of cards in the deck ($0 < n \le 64$) and $c$ is the number of cards Jacob will definitely draw ($0 \le c < n$). The second line contains $n$ distinct integers $a_ i$ ($0 \le a_ i \le 10000$) - the numbers written on the cards in the deck, which may be given in any order.

-----Output-----
Output the expected score under Jacob’s strategy. Your answer will be considered correct if its absolute or relative error does not exceed $10^{-5}$.

-----Examples-----
Sample Input 1:
2 1
0 1
Sample Output 1:
0.500000

Sample Input 2:
4 2
0 4 8 6
Sample Output 2:
5.500000

Sample Input 3:
15 7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Sample Output 3:
11.266667
user: Given a permutation $A = (a_1, a_2, \dots , a_ N)$ of the integers $1, 2, \dots , N$, we define the greedily increasing subsequence (GIS) in the following way.

Let $g_1 = a_1$. For every $i > 1$, let $g_ i$ be the leftmost integer in $A$ that is strictly larger than $g_{i-1}$. If for a given $i$ there is no such integer, we say that the GIS of the sequence is the sequence $(g_1, g_2, ..., g_{i - 1})$.

For example, consider the permutation $(2, 3, 1, 5, 4, 7, 6)$. First, we have $g_1 = 2$. The leftmost integer larger than $2$ is $3$, so $g_2 = 3$. The leftmost integer larger than $3$ is $5$ ($1$ is too small), so $g_3 = 5$. Finally, $g_4 = 7$. Thus, the GIS of $(2, 3, 1, 5, 4, 7, 6)$ is $(2, 3, 5, 7)$.

Given a sequence $G = (g_1, g_2, \dots , g_ L)$, how many permutations $A$ of the integers $1, 2, \dots , N$ have $G$ as its GIS?

-----Input-----
The first line of input contains the integers $1 \le N \le 10^6$, the number of elements of the permutation $A$, and $1 \le L \le 10^6$, the length of the sequence $G$.

The next line contains $L$ positive integers between $1$ and $N$, the elements $g_1, \dots , g_ L$ of the sequence $G$.

-----Output-----
Output a single integer: the number of $N$-element permutations having the given sequence as its GIS. Since this number may be large, output it modulo the prime number $10^9 + 7$.

-----Examples-----
Sample Input 1:
5 1
1
Sample Output 1:
0

Sample Input 2:
5 1
5
Sample Output 2:
24

Sample Input 3:
5 3
2 4 5
Sample Output 3:
8
user: You and your classmates are going on an exciting field trip to a downtown museum. Because the museum is an hour away, three buses of identical capacity and a van are dispatched as a means of transportation to the museum and back. The buses will first start loading only students, and once all students have been loaded then teachers will begin to fill in the remaining spots on the buses. Any remaining teachers will ride on the van. To make the bus ride more exciting, all the students are hoping for a “teacher free bus ride”! A teacher free bus ride is when none of the teachers are on a bus.

Students are grouped in $n$ class sections of different sizes. Each class section is assigned a number from $1$ to $n$. All students in one class section must ride on the same bus. The buses will board class sections in increasing order by number. In other words, the first bus will load sections numbered $1$ to $i$, the second bus will load sections numbered $i+1$ to $j$, and the third bus will load the sections numbered $j+1$ to $n$. Every bus must have at least one class section assigned to it.

Given the sizes of each of the class sections, determine if it is possible to load students onto $3$ identical buses and end up with a “teacher free bus ride!”

-----Input-----
The first line of input contains one integer $N$, the number of class sections ($3 \le N \le 1000000$). The second line of input contains $N$ integers, the $i^{\text {th}}$ integer represents the size of class section with number $i$. Class section sizes can range from $[1, 10000]$.

-----Output-----
If it is possible to load the students onto three identical buses in the above-described fashion and have a teacher free bus ride, then output two integers $i$ and $j$ ($1 \le i < j < n$) where $i$ is the number of the class section which is to be loaded last into the first bus, and $j$ is the class section which is to be loaded last into the second bus. We can assume the third bus will load class sections $j+1$ to $n$.

If it is not possible, print “-1”.

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

Sample Input 2:
3
9 10 11
Sample Output 2:
-1

Sample Input 3:
9
1 2 3 1 2 3 1 2 3
Sample Output 3:
3 6
user: Dividing two numbers and computing the decimals is an extremely difficult task. Luckily, dividing a number by a “special” number is very easy (at least for us humans)!

We will define the set of “special” numbers $S=\{ 10^K\} $ for all non-negative integers $K$, i.e. $\{ 1,10,100,\ldots \} $.

Given a large numbers $N$ and a “special” large number $M$, what does the decimal representation of\[ \frac{N}{M} \]

look like?

-----Input-----
The first line of input contains 2 integers $N$, $M$, where $1\leq N, M\leq 10^{10^6}$, and $M\in S$.

-----Output-----
Print the exact decimal preresentation of $\frac{N}{M}$, i.e. every digit, without trailing zeroes; if the quotient is less than $1$, print one leading zero (see sample input).

-----Examples-----
Sample Input 1:
92746237
100000
Sample Output 1:
927.46237

Sample Input 2:
100000
100
Sample Output 2:
1000

Sample Input 3:
1234500
10000
Sample Output 3:
123.45