meetforever/GRPO_CL huggingface dataset:
user: The home office of Labyrinthian Inc. has installed a new system of security badges and electronic door locks. Each badge is assigned an ID number, and the idea was that electronic locks on each door should allow access only to personnel whose ID number indicated that they had appropriate security clearance to enter that room, hallway, closet, or whatever lay on the other side of the door. 

The contract for the lock system, however, was put out to the lowest bidder, who clearly misunderstood the intention. Instead of each lock storing a list of permitted ID numbers, instead each lock stores exactly two numbers, a lower and upper bound, and permits passage to badges whose number lies between those bounds. For example, a lock keyed as $(25, 29)$ would pass only badges $25, 26, 27, 28,$ and $29$.

Complicating the matter is the fact that lock on each side of the door can be keyed differently, so a person who is able to pass through the door in one direction might not be able to return once the door has closed behind them.

The results have been frustrating (and occasionally entertaining – videos of everyone in the company trying to find a way to the cafeteria at noon have gone viral on social media).

It has become a major task, when hiring or promoting any employee, to find a badge number that will actually get them from the front door to their new office.

Write a program to determine how many badge numbers will permit passage from one given room to another.

-----Input-----
The first line of input will contain integers $N$, $L$, and $B$, denoting the number of rooms, of locks, and of badge numbers, respectively. $2 \leq N \leq 1000$, $1 \leq L \leq 5000$, $1 \leq B \leq 10^9$

The next line of input will contain two integers, $S$ and $D$, $1 \leq S \leq N$, $1 \leq D \leq N$, $S \neq D$, denoting the starting and destination rooms that we are interested in.

This is followed by $L$ lines, each describing a lock as four integers:\[ a \; b \; x \; y \]

indicating that a lock permits passage from room $a$ to room $b$ (but not from $b$ to $a$) for badges numbered from $x$ to $y$, inclusive. It is guaranteed that $1 \leq a, b \leq N$, $a \neq b$, $1 \leq x \leq B$, $1 \leq y \leq B$, $x \leq y$, and no $(a,b)$ pair will occur more than once, although both $(a,b)$ and $(b,a)$ may occur within separate lines.

-----Output-----
Print a single line indicating the number of badge ID numbers permitting passage from room $S$ to room $D$

-----Examples-----
Sample Input:
4 5 10
3 2
1 2 4 7
3 1 1 6
3 4 7 10
2 4 3 5
4 2 8 9
Sample Output:
5
user: Bob is completing a true/false worksheet, consisting of a list of $n$ problems where each answer is either “true” or “false”. The problems are numbered from $1$ to $n$. They are too hard for Bob, so the TA, Alice, has given Bob $m$ hints. For each hint $i$, Alice gives Bob an (inclusive) range of questions $[l_ i, r_ i]$, and tells him either “all answers in the range are the same” (in other words, either all are “true”, or all are “false”); or “not all of the answers in the range are the same.” Help Bob count how many different answer sequences satisfy the given hints. Since this number may be huge, print the answer modulo $10^9+7$.

-----Input-----
The first line of the input contains two space-separated integers $n$ and $m$ $(1 \le n \le 5000, 1 \le m \le 1000000)$, the number of problems and number of hints, respectively. The next $m$ lines each encode a hint, and contain two space-separated integers $l_ i$ and $r_ i$ $(1\leq l_ i \leq r_ i\leq n)$ followed by either the word same, if all answers in the range are the same, or different, if all answers in the range are not the same (i.e., at least one answer is “true” and at least one other answer is “false”).

-----Output-----
Print the number of different answer sequences satisfying all the hints, modulo $10^9+7$.

-----Sample Explanation-----
In the first sample, the four possible sequences consistent with the hints are 00000, 10000, 01111, and 11111 where 0 stands for a “false” answer and 1 stands for a “true” answer. In the second sample, the third hint conflicts with the first two hints, so no answer sequence exists consistent with all hints.

-----Examples-----
Sample Input:
5 2
2 4 same
3 5 same
Sample Output:
4
user: One day your boss explains to you that he has a bunch of computer networks that are currently unreachable from each other, and he asks you, the cable expert’s assistant, to adjoin the networks to each other using new cables. Existing cables in the network cannot be touched.

He has asked you to use as few cables as possible, but the length of the cables used does not matter to him, since the cables are optical and the connectors are the expensive parts. Your boss is rather picky on cable usage, so you know that the already existing networks have as few cables as possible.

Due to your humongous knowledge of computer networks, you are of course aware that the latency for an information packet travelling across the network is proportional to the number of hops the packet needs, where a hop is a traversal along a single cable. And since you believe a good solution to your boss’ problem may earn you that long wanted promotion, you decide to minimise the maximum number of hops needed between any pair of network nodes.

-----Input-----
On the first line, you are given two positive integers, the number $1 \leq c \leq 10^5$ of computers and the number $0 \leq \ell \leq c-1$ of existing cables. Then follow $\ell $ lines, each line consisting of two distinct integers $a$ and $b$, the two computers the cables connect. You may assume that every computer has a unique name between $0$ and $c-1$.

-----Output-----
The maximum number of hops in the resulting network.

-----Examples-----
Sample Input:
6 4
0 1
0 2
3 4
3 5
Sample Output:
3
user: Mirko found a wooden board and $N$ nails in his attic. Mirko hammered the nails into the board as fast as possible. The board can be modeled by a coordinate plane and the nails as points in it. No two nails have the same $x$- or the same $y$-coordinate.

In order to keep having fun, Mirko stole his sister’s elastic hair band, spread it over all nails and then let go. The elastic, naturally, tightened around the nails.

Mirko then repeats these steps while there are at least three nails in the board:
 - Write down the area of the shape enclosed by the hair band.
 - Picks the leftmost, rightmost, topmost or bottommost nail in the board.
 - Remove the chosen nail from the board; the elastic tightens again around the remaining nails.

Write a program that calculates the numbers written in step 1 of each iteration, if we know the nail Mirko picks in step 2 of each iteration.

-----Input-----
The first line contains the integer $N$ $(3 \leq N \leq 300000)$, the number of nails.

Each of the following $N$ lines contains two integers separated by a space, the coordinates of a nail. All coordinates will be between 1 and $1000000000$. No two nails will share the same $x$- or $y$-coordinate. The next line contains $N-2$ letters ’L’, ’R’, ’U’ or ’D’. The letters represent the nails Mirko picked in order:
 - ’L’ for the leftmost nail (smallest $x$-coordinate),
 - ’R’ for the rightmost nail (largest $x$-coordinate),
 - ’U’ for the topmost nail (largest $y$-coordinate),
 - ’D’ for the bottommost nail (smallest $y$-coordinate).

-----Output-----
Output $N-2$ numbers, each on a separate line. The numbers are, in order, the areas that Mirko wrote down. Output numbers with one digit after the decimal point.

-----Examples-----
Sample Input:
5
1 4
2 2
4 1
3 5
5 3
LUR
Sample Output:
9.0
6.5
2.5
user: Given an undirected, unweighted, connected graph, where each edge is colored either blue or red, determine whether a spanning tree with exactly $k$ blue edges exists.

-----Input-----
There will be a single test case in the input. Each test case will begin with a line with three integers:

$n \ m \ k$

Where $n$ ($2 \le n \le 1000$) is the number of nodes in the graph, $m$ (limited by the structure of the graph) is the number of edges in the graph, and $k$ ($0 \le k < n$) is the number of blue edges desired in the spanning tree. Each of the next $m$ lines will contain three elements, describing the edges:

$c \ f \ t$

Where $c$ is a character, either capital R or capital B, indicating the color of the edge, and $f$ and $t$ are integers ($1 \le f, t \le n, t \ne f$) indicating the nodes that edge goes from and to. The graph is guaranteed to be connected, and there is guaranteed to be at most one edge between any pair of nodes.

-----Output-----
Output a single line, containing $1$ if it is possible to build a spanning tree with exactly $k$ blue edges, and $0$ if it is not possible.

-----Examples-----
Sample Input:
3 3 2
B 1 2
B 2 3
R 3 1
Sample Output:
1
user: Jimmy and his friends like to visit large theme parks. In the current theme park there are many roller coasters which then are categorized by Jimmy. He assigns a fun value to each coaster; however, the fun decreases with each run.

More formally: for a specific roller coaster $i$, Jimmy assigns two fun coefficients $a_ i$ and $b_ i$. While riding this roller coaster for the $k$-th time, Jimmy gains a fun value of $f(i,k) = a_ i - (k-1)^2 \cdot b_ i$. If $f(i,k)$ is non-positive, riding the roller coaster is no longer fun.

Jimmy tries to maximize the total fun until he leaves the park. Can you tell Jimmy how much fun he can gain for a given time?

-----Input-----
The input consists of a single test case.

The first line contains the integer $N$, where $N$ is the amount of different roller coasters in the theme park ($0< N\le 100$).

The following $N$ lines contain the integers $a_ i$, $b_ i$ and $t_ i$ where $a_ i$ and $b_ i$ are the fun coefficients as specified above and $t_ i$ is the time for a single ride with the $i$-th roller coaster ($0\le a_ i \le 1000$; $0\le b_ i \le 1000$; $0 < t_ i \le 25000$).

The next line contains a positive integer $Q$ denoting the number of times that Jimmy is visiting the park ($0\le Q \le 1000$). Each of the following $Q$ lines contains an integral time $T_ i$ that Jimmy spends during his $i$-th visit ($0\le T_ i \le 25000$).

-----Output-----
For each of the $Q$ possible times, print one line containing the maximal total fun value if Jimmy spends $T_ i$ minutes in the theme park.

-----Examples-----
Sample Input:
2
5 0 5
7 0 7
4
88
5
6
7
Sample Output:
88
5
5
7
user: Your state has just purchased a large, unspoiled tract of land, and wishes to turn it into a nature park with hiking trails. The land has $n$ places of interest to which guests may wish to hike, and of these, $k$ are very special. The state wishes to connect these places with hiking trails. There are $m$ candidate hiking trails to choose from that directly connect two places of interest with various costs. There are some constraints for choosing the trails. First, there must be exactly one way to hike from any place to any other place. Second, exactly $w$ of the trails must directly connect a special place with a regular place. Of course, the state wishes to minimize the cost of blazing these trails.

-----Input-----
Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. The first line of input will contain four integers $n$, $m$, $k$ and $w$, where $n$ ($2 \le n \le 2 \cdot 10^5$) is the number of places, $m$ ($1 \le m \le 5 \cdot 10^5$) is the number of potential direct trails between places, $k$ ($1 \le k < n$) is the number of special places, and $w$ ($1 \le w \le n-1$) is the number of special-nonspecial direct trails the state wishes to blaze. The places are numbered $1$ to $n$.

Each of the next $k$ lines holds a single integer $s$ ($1 \le s \le n$) indicating the special places. These values will be unique and will be in ascending order.

Each of the next $m$ lines will describe a potential trail that the state could blaze. Each of these lines will consist of three integers, $a$, $b$ and $c$, where the trail would go between places $a$ and $b$ ($1 \le a,b \le n, a \ne b$) and would cost $c$ ($1 \le c \le 10^5$). No two places will have more than one potential trail between them, and a trail from $a$ to $b$ is the same as a trail from $b$ to $a$.

-----Output-----
Output a single integer, which is the minimum total cost for the state to blaze trails in their new park subject to their constraints, or $-1$ if it isn’t possible.

-----Examples-----
Sample Input:
3 3 1 2
2
1 2 2
1 3 1
2 3 3
Sample Output:
5
user: Mirko likes to play with strings of characters, but this time he has taken it too far – he put an “explosion” in the string! An explosion is a series of characters which, if found in the vicinity of fire, explodes and starts a chain reaction.

Mirko, being as negligent as he usually is, forgot that his string contained an explosion and placed it near a candlelight. Thus the chain reaction began.

The chain reaction takes place in the following way:
 - if a string contains explosions, they all explode and a new string is formed by concatenating the pieces without the exploding parts
 - this concatenation could possibly create new explosions
 - the chain reaction repeats while there are explosions in the string

Now Mirko wants to know whether anything will be left after this series of chain reactions. If nothing remains, output “FRULA” (without quotes). If, by any chance, something is left, output the final string remaining after all the reactions.

Please note: The explosion will not contain two equal characters.

-----Input-----
The first line of input contains Mirko’s string, ($1 \leq |\text {Mirko’s string}| \leq 1\ 000\ 000$).

The second line of input contains the explosion string, ($1 \leq |\text {explosion}| \leq 36$).

Both Mirko’s string and the explosion string consist of uppercase and lowercase letters of the English alphabet and digits 0, 1, …, 9. The characters in the explosion string are all different.

-----Output-----
The first and only line of output must contain the final string remaining after all the reactions as stated in the task.

Clarification of the second example: Firstly, the bombs on positions $1$ and $6$ explode. Then we are left with ****1****2ab (where * marks the character that exploded) and when that string is put together, we get 12ab. Sadly, that is an explosion all over again so it disappears.

-----Examples-----
Sample Input:
mirkovC4nizCC44
C4
Sample Output:
mirkovniz
user: In a single day, $N$ of Luka’s trucks travel a specific highway. The highway has a number of exits and entrances. An exit with a particular number is in the same location as the entrance with that number.

Upon entering the highway, a truck driver receives a ticket which indicates the entrance he used. When exiting, the driver pays a toll equal to the absolute difference of the entrance and exit numbers. For example, if a ticket says he used entrance $30$, then exiting at exit $12$ will cost him $18$.

Luka has figured out a way to save toll money that his company daily spends. Any two drivers can meet on the highway and exchange tickets, even if their routes don’t overlap. Tickets can be exchanged an arbitrary number of times.

However, a driver cannot use an exit if his ticket says he used the same entrance, since that would be suspicious.

Write a program that calculates the least total amount of tolls that the drivers can achieve by exchanging tickets.

-----Input-----
The first line contains the integer $N$ $(1 \leq N \leq 100000)$, the number of trucks. Each of the following $N$ lines contains two distinct integers between $1$ and $1000000000$. These are in order the entrance and exit numbers of one truck.

No two trucks will use the same highway entrance or the same exit.

-----Output-----
Output the least total amount of tolls Luka’s company must pay.

-----Examples-----
Sample Input:
3
3 65
45 10
60 25
Sample Output:
32
user: Young Mirka is an amateur musician. She plays the multi-piano. $A$ multi-piano consists of an infinite number of multi-keys, denoted with integers that can be interpreted as the pitch. $A$ multi-composition (a composition written for a multi-piano) can be represented with a finite array of integers, where integers denote the order of multi-keys to press in order to play the multi-composition.

Young Mirka has heard a multi-composition on the multi-radio and now she wants to play it. Unfortunately, she cannot hear exactly which key was pressed, but instead she can hear whether the pressed multi-key was higher, lower or equal to the previously played key (a higher key is denoted with a larger number). Therefore she has decided to play the composition in the following way:
 - before playing, she will choose one non-negative integer $K$
 - in the beginning, she will play the correct multi-key (her multi-teacher told her which multi-key that is)
 - when she hears that the multi-key played in the multi-composition is higher than the previous multi-key played in the multi-composition, she will play the multi-key denoted with the integer larger than the multi-key she played previously by $K$
 - analogously, when she hears that the multi-key played in the multi-composition is lower than the previous multi-key played in the multi-composition, she will play the multi-key denoted with the integer smaller than the multi-key she played previously by $K$
 - when she hears that the multi-key played in the multi-composition is equal to the previous multi-key played in the multi-composition, she will repeat the multi-key she played previously

Notice that, when Mirka is playing, she does not compare the pitch of the keys she played to the pitch of the keys from the composition.

Help Mirka choose the integer $K$ in order to hit as many correct pitches as possible.

-----Input-----
The first line of input contains the integer $N$ ($2 \leq N \leq 10^6$), the number of multi-keys in the multi- composition on the multi-radio.

The second line of input contains $N$ integers $a_ i$ ($-10^9 \leq a_ i \leq 10^9$), the multi-keys played in the multi-composition.

-----Output-----
The first line of output must contain the maximum number of multi-keys that Mirka can play correctly. The second line of output must contain the non-negative number $K$ that Mirka must choose in order to hit as many correct pitches as possible. The number must be smaller than or equal to $2 \cdot 10^9$. The required number does not have to be unique, but will surely exist within the given constraints.

-----Examples-----
Sample Input:
5
1 2 0 3 1
Sample Output:
3
2
user: Matthew the physicist studies the quantum electro-dynamics of a silicon-based rectangular microchip. The microchip consists of a very large $N \times M$ grid of electrons. Each electron has either positive (up) or negative (down) spin, denoted by $+$ and $-$ respectively.

Matthew does not know the spin of all the electrons, but he has done $K$ measurements. In the $i$-th measurement, he discovered that the electron at position $(y_ i, x_ i)$ has a given spin $s_ i$. He also knows that in each $2\times 2$ subgrid, there are equally many electrons with positive and negative spin. He wants to know whether he can recover the state of every electron based on his measurements. If not, he would like to know how many possible states are consistent with his measurements. For classified reasons, he wants the answer modulo $10^9 + 7$.

-----Input-----
The first line contain three numbers $N$, $M$ and $K$: the height of the grid, the width of the grid and the number of measurements. The next $K$ lines contain a spin $s_ i$ where $s_ i$ is either $+$ or $-$, and two numbers $1 \leq y_ i \leq N$ and $1 \leq x_ i \leq M$ – the coordinates of the electron. Matthew never did two measurments at the exact same location.

We always have $1 \leq N, M \leq 10^9$ and $0 \leq K \leq 100000$.

-----Output-----
Output the total number of valid states consistent with Matthew’ measurements modulo $10^9 + 7$.

-----Examples-----
Sample Input:
2 4 4
+ 1 1
- 1 2
+ 1 3
- 1 4
Sample Output:
2
user: Consider a rooted tree with $n$ nodes, numbered $1..n$. Each node will have a fixed integer $b$, and for each, a uniform random real number is chosen in the interval $[0..b]$.

What is the probability that the random numbers chosen cause the tree to form a Heap (i.e., the random value in each node is less than the random values in its children)?

This probability can always be expressed as a rational number $\frac{P}{Q}$, with $Q{\not\equiv }0 \pmod{10^9{+}7}$. You are to output the probability as $P{\cdot }Q^{-1} \bmod {10^9{+}7}$, where $Q^{-1}$ is an integer, which is the multiplicative inverse of $Q$ modulo $10^9{+}7$ ($Q\! \cdot \! Q^{-1}\! \equiv \! 1 \pmod{10^9{+}7}$). (Note: $P{\cdot }Q^{-1}\bmod {10^9{+}7}$ does not depend on whether $P$ and $Q$ are relatively prime, only on their ratio $\frac{P}{Q}$.)

-----Input-----
Each test case will begin with a line with a single integer $n$ ($1\! \le \! n\! \le \! 300$), which is the number of nodes in the tree.

Each of the next $n$ lines will contain a pair of space-separated integers $b$ ($1\! \le \! b\! \le \! 10^9$) and $p$ ($0\! \le \! p\! \le \! n$) describing a node of the tree, where $b$ is the fixed integer value in the node and $p$ is the node number of its parent. The nodes are listed in order; node $1$ is first, then node $2$, and so on. A single node will have a parent $p{=}0$. This is the root of the tree.

-----Output-----
Output a single integer, which is the probability expressed as $(P{\cdot }Q^{-1}) \bmod ({10^9{+}7})$.

-----Examples-----
Sample Input:
2
1000000000 0
1000000000 1
Sample Output:
500000004
user: David is looking to book some travel over the world. There are $n$ countries that he can visit, and $m$ flights that are available. The $i$th flight goes from country $a_ i$ to country $b_ i$. It departs at time $s_ i$, and lands at time $e_ i$. 

David is currently at the airport in country $1$, and the current time is $0$, and he would like to travel country $n$. He does not care about the total amount of time needed to travel, but he really hates waiting in the airport. If he waits $t$ seconds in an airport, he gains $t^2$ units of frustration. Help him find an itinerary that minimizes the sum of frustration.

-----Input-----
The first line of input contains two space-separated integers $n$ and $m$ ($1 \le n,m \le 200000$).

Each of the next $m$ lines contains four space-separated integers $a_ i$, $b_ i$, $s_ i$, and $e_ i$ ($1 \le a_ i, b_ i \le n$; $0 \le s_ i \le e_ i \le 10^6$).

A flight might have the same departure and arrival country.

No two flights will have the same arrival time, or have the same departure time. In addition, no flight will have the same arrival time as the departure time of another flight. Finally, it is guaranteed that there will always be a way for David to arrive at his destination.

-----Output-----
Print, on a single line, the minimum sum of frustration.

-----Examples-----
In the first sample, it is optimal to take this sequence of flights:
 - Flight $5$. Goes from airport $1$ to airport $2$, departing at time $3$, arriving at time $8$.
 - Flight $3$. Goes from airport $2$ to airport $1$, departing at time $9$, arriving at time $12$.
 - Flight $7$. Goes from airport $1$ to airport $3$, departing at time $13$, arriving at time $27$.
 - Flight $8$. Goes from airport $3$ to airport $5$, deparing at time $28$, arriving at time $100$.

The frustration for each flight is $3^2, 1^2, 1^2,$ and $1^2$, respectively. Thus, the total frustration is $12$.

Note that there is an itinerary that gets David to his destination faster. However, that itinerary has a higher total frustration.

-----Examples-----
Sample Input:
5 8
1 2 1 10
2 4 11 16
2 1 9 12
3 5 28 100
1 2 3 8
4 3 20 21
1 3 13 27
3 5 23 24
Sample Output:
12