vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Title: One Occurrence

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
You are given an array $a$ consisting of $n$ integers, and $q$ queries to it. $i$-th query is denoted by two integers $l_i$ and $r_i$. For each query, you have to find any integer that occurs exactly once in the subarray of $a$ from index $l_i$ to index $r_i$ (a subarray is a contiguous subsegment of an array). For example, if $a = [1, 1, 2, 3, 2, 4]$, then for query $(l_i = 2, r_i = 6)$ the subarray we are interested in is $[1, 2, 3, 2, 4]$, and possible answers are $1$, $3$ and $4$; for query $(l_i = 1, r_i = 2)$ the subarray we are interested in is $[1, 1]$, and there is no such element that occurs exactly once.

Can you answer all of the queries?

Input Specification:
The first line contains one integer $n$ ($1 \le n \le 5 \cdot 10^5$).

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 5 \cdot 10^5$).

The third line contains one integer $q$ ($1 \le q \le 5 \cdot 10^5$).

Then $q$ lines follow, $i$-th line containing two integers $l_i$ and $r_i$ representing $i$-th query ($1 \le l_i \le r_i \le n$).

Output Specification:
Answer the queries as follows:

If there is no integer such that it occurs in the subarray from index $l_i$ to index $r_i$ exactly once, print $0$. Otherwise print any such integer.

Demo Input:
['6\n1 1 2 3 2 4\n2\n2 6\n1 2\n']

Demo Output:
['4\n0\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Write a function that accepts two parameters, i) a string (containing a list of words) and ii) an integer (n).  The function should alphabetize the list based on the nth letter of each word.

The letters should be compared case-insensitive. If both letters are the same, order them normally (lexicographically), again, case-insensitive.

example:
```javascript 
function sortIt('bid, zag', 2) //=> 'zag, bid'
```
```ruby 
function sortIt('bid, zag', 2) //=> 'zag, bid'
```
```python 
function sortIt('bid, zag', 2) #=> 'zag, bid'
```

The length of all words provided in the list will be >= n.  The format will be "x, x, x". In Haskell you'll get a list of `String`s instead.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You will be given an array of non-negative integers and positive integer bin width. 

Your task is to create the Histogram method that will return histogram data corresponding to the input array. The histogram data is an array that stores under index i the count of numbers that belong to bin i. The first bin always starts with zero. 

On empty input you should return empty output.

Examples:

For input data [1, 1, 0, 1, 3, 2, 6] and binWidth=1 the result will be [1, 3, 1, 1, 0, 0, 1] as the data contains single element "0", 3 elements "1" etc.
For the same data and binWidth=2 the result will be [4, 2, 0, 1]
For input data [7] and binWidth=1 the result will be [0, 0, 0, 0, 0, 0, 0, 1]

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The zombie apocalypse is here and Chef is stuck at an old construction site. The site is surrounded by walls on three sides. On the fourth side is a fence where $N$ zombies are standing in a row. The zombies are numbered from $1$ to $N$ from left to right. Zombie $i$ has $Z_{i}$ health points initially.

Luckily there are $M$ cranes Chef has access to. The $i^{th}$ crane carries $K_{i}$ construction beams. Chef can drop any number $≥ 0$ and $≤ K_{i}$ of these beams from crane $i$ and they will hit all zombies whose numbers lie between $L_{i}$ to $R_{i}$ both inclusive. A single beam decreases the health of all zombies it hits by $1$ point. If a zombie's health equals $0$ after being hit it is considered dead.

Can Chef kill all the zombies using the beams? If yes, what is the minimum number of beams that Chef has to drop to achieve this?

Warning: Large I/O, it is advisable to use fast I/O methods.

------  Input: ------
The first line contains $T$, number of testcases. 
The first line of each test case contains two integers $N$ and $M$.
The second line of each test case contains $N$ integers $Z_{1}, Z_{2}, ..., Z_{N}$.
$M$ lines follow. The $i^{th}$ line contains $3$ integers $L_{i}$, $R_{i}$ and $K_{i}$.

------  Output: ------
For each test case, if it is possible for Chef to kill all the zombies print a single line containing "YES" followed by the minimum number of beams he needs to drop. If it is impossible, print "NO" instead. (Note that the judge is case-sensitive)

------  Constraints  ------
$1 ≤ T ≤ 10$
$1 ≤ N, M ≤ 10^{5}$
Sum of $N$ over all test cases $≤ 3 \cdot 10^{5}$
Sum of $M$ over all test cases $≤ 3 \cdot 10^{5}$
$1 ≤ Z_{i} ≤ 10^{9}$
$1 ≤ L_{i} ≤ R_{i} ≤ N$
$1 ≤ K_{i} ≤ 10^{9}$

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

------  Sample Output: ------
YES 6
NO
	
------  Explanation: ------
Case 1: One possible way is for Chef to drop the only beam from crane 2, 1 beam from crane 3, 1 beam from crane 4 and all 3 beams from crane 5.
Case 2: Zombie 1 and 3 can be killed but zombie 2 remains at health 1 even if all the beams are dropped.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Art Union

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
A well-known art union called "Kalevich is Alive!" manufactures objects d'art (pictures). The union consists of *n* painters who decided to organize their work as follows.

Each painter uses only the color that was assigned to him. The colors are distinct for all painters. Let's assume that the first painter uses color 1, the second one uses color 2, and so on. Each picture will contain all these *n* colors. Adding the *j*-th color to the *i*-th picture takes the *j*-th painter *t**ij* units of time.

Order is important everywhere, so the painters' work is ordered by the following rules:
 -  Each picture is first painted by the first painter, then by the second one, and so on. That is, after the *j*-th painter finishes working on the picture, it must go to the (*j*<=+<=1)-th painter (if *j*<=&lt;<=*n*); -  each painter works on the pictures in some order: first, he paints the first picture, then he paints the second picture and so on; -  each painter can simultaneously work on at most one picture. However, the painters don't need any time to have a rest; -  as soon as the *j*-th painter finishes his part of working on the picture, the picture immediately becomes available to the next painter. 
Given that the painters start working at time 0, find for each picture the time when it is ready for sale.

Input Specification:
The first line of the input contains integers *m*,<=*n* (1<=≤<=*m*<=≤<=50000,<=1<=≤<=*n*<=≤<=5), where *m* is the number of pictures and *n* is the number of painters. Then follow the descriptions of the pictures, one per line. Each line contains *n* integers *t**i*1,<=*t**i*2,<=...,<=*t**in* (1<=≤<=*t**ij*<=≤<=1000), where *t**ij* is the time the *j*-th painter needs to work on the *i*-th picture.

Output Specification:
Print the sequence of *m* integers *r*1,<=*r*2,<=...,<=*r**m*, where *r**i* is the moment when the *n*-th painter stopped working on the *i*-th picture.

Demo Input:
['5 1\n1\n2\n3\n4\n5\n', '4 2\n2 5\n3 1\n5 3\n10 1\n']

Demo Output:
['1 3 6 10 15 ', '7 8 13 21 ']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Young wilderness explorers set off to their first expedition led by senior explorer Russell. Explorers went into a forest, set up a camp and decided to split into groups to explore as much interesting locations as possible. Russell was trying to form groups, but ran into some difficulties...

Most of the young explorers are inexperienced, and sending them alone would be a mistake. Even Russell himself became senior explorer not long ago. Each of young explorers has a positive integer parameter $e_i$ — his inexperience. Russell decided that an explorer with inexperience $e$ can only join the group of $e$ or more people.

Now Russell needs to figure out how many groups he can organize. It's not necessary to include every explorer in one of the groups: some can stay in the camp. Russell is worried about this expedition, so he asked you to help him.


-----Input-----

The first line contains the number of independent test cases $T$($1 \leq T \leq 2 \cdot 10^5$). Next $2T$ lines contain description of test cases.

The first line of description of each test case contains the number of young explorers $N$ ($1 \leq N \leq 2 \cdot 10^5$).

The second line contains $N$ integers $e_1, e_2, \ldots, e_N$ ($1 \leq e_i \leq N$), where $e_i$ is the inexperience of the $i$-th explorer.

It's guaranteed that sum of all $N$ doesn't exceed $3 \cdot 10^5$.


-----Output-----

Print $T$ numbers, each number on a separate line.

In $i$-th line print the maximum number of groups Russell can form in $i$-th test case.


-----Example-----
Input
2
3
1 1 1
5
2 3 1 2 2

Output
3
2



-----Note-----

In the first example we can organize three groups. There will be only one explorer in each group. It's correct because inexperience of each explorer equals to $1$, so it's not less than the size of his group.

In the second example we can organize two groups. Explorers with inexperience $1$, $2$ and $3$ will form the first group, and the other two explorers with inexperience equal to $2$ will form the second group.

This solution is not unique. For example, we can form the first group using the three explorers with inexperience equal to $2$, and the second group using only one explorer with inexperience equal to $1$. In this case the young explorer with inexperience equal to $3$ will not be included in any group.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
# A wolf in sheep's clothing

Wolves have been reintroduced to Great Britain. You are a sheep farmer, and are now plagued by wolves which pretend to be sheep. Fortunately, you are good at spotting them. 

Warn the sheep in front of the wolf that it is about to be eaten. Remember that you are standing **at the front of the queue** which is at the end of the array:

```
[sheep, sheep, sheep, sheep, sheep, wolf, sheep, sheep]      (YOU ARE HERE AT THE FRONT OF THE QUEUE)
   7      6      5      4      3            2      1
```

If the wolf is the closest animal to you, return `"Pls go away and stop eating my sheep"`. Otherwise, return `"Oi! Sheep number N! You are about to be eaten by a wolf!"` where `N` is the sheep's position in the queue.

**Note:** there will always be exactly one wolf in the array.

## Examples

```python
warn_the_sheep(["sheep", "sheep", "sheep", "wolf", "sheep"]) == 'Oi! Sheep number 1! You are about to be eaten by a wolf!'

warn_the_sheep(['sheep', 'sheep', 'wolf']) == 'Pls go away and stop eating my sheep'
```

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Merge sort is a well-known sorting algorithm. The main function that sorts the elements of array a with indices from [l, r) can be implemented as follows:  If the segment [l, r) is already sorted in non-descending order (that is, for any i such that l ≤ i < r - 1 a[i] ≤ a[i + 1]), then end the function call;  Let $\operatorname{mid} = \lfloor \frac{l + r}{2} \rfloor$;  Call mergesort(a, l, mid);  Call mergesort(a, mid, r);  Merge segments [l, mid) and [mid, r), making the segment [l, r) sorted in non-descending order. The merge algorithm doesn't call any other functions. 

The array in this problem is 0-indexed, so to sort the whole array, you need to call mergesort(a, 0, n).

The number of calls of function mergesort is very important, so Ivan has decided to calculate it while sorting the array. For example, if a = {1, 2, 3, 4}, then there will be 1 call of mergesort — mergesort(0, 4), which will check that the array is sorted and then end. If a = {2, 1, 3}, then the number of calls is 3: first of all, you call mergesort(0, 3), which then sets mid = 1 and calls mergesort(0, 1) and mergesort(1, 3), which do not perform any recursive calls because segments (0, 1) and (1, 3) are sorted.

Ivan has implemented the program that counts the number of mergesort calls, but now he needs to test it. To do this, he needs to find an array a such that a is a permutation of size n (that is, the number of elements in a is n, and every integer number from [1, n] can be found in this array), and the number of mergesort calls when sorting the array is exactly k.

Help Ivan to find an array he wants!


-----Input-----

The first line contains two numbers n and k (1 ≤ n ≤ 100000, 1 ≤ k ≤ 200000) — the size of a desired permutation and the number of mergesort calls required to sort it.


-----Output-----

If a permutation of size n such that there will be exactly k calls of mergesort while sorting it doesn't exist, output  - 1. Otherwise output n integer numbers a[0], a[1], ..., a[n - 1] — the elements of a permutation that would meet the required conditions. If there are multiple answers, print any of them.


-----Examples-----
Input
3 3

Output
2 1 3 
Input
4 1

Output
1 2 3 4 
Input
5 6

Output
-1

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Monocarp wants to watch $n$ videos. Each video is only one minute long, but its size may be arbitrary. The $i$-th video has the size $a_i$ megabytes. All videos are published on the Internet. A video should be downloaded before it can be watched. Monocarp has poor Internet connection — it takes exactly $1$ minute to download $1$ megabyte of data, so it will require $a_i$ minutes to download the $i$-th video.

Monocarp's computer has a hard disk of $m$ megabytes. The disk is used to store the downloaded videos. Once Monocarp starts the download of a video of size $s$, the $s$ megabytes are immediately reserved on a hard disk. If there are less than $s$ megabytes left, the download cannot be started until the required space is freed. Each single video can be stored on the hard disk, since $a_i \le m$ for all $i$. Once the download is started, it cannot be interrupted. It is not allowed to run two or more downloads in parallel.

Once a video is fully downloaded to the hard disk, Monocarp can watch it. Watching each video takes exactly $1$ minute and does not occupy the Internet connection, so Monocarp can start downloading another video while watching the current one.

When Monocarp finishes watching a video, he doesn't need it on the hard disk anymore, so he can delete the video, instantly freeing the space it occupied on a hard disk. Deleting a video takes negligible time.

Monocarp wants to watch all $n$ videos as quickly as possible. The order of watching does not matter, since Monocarp needs to watch all of them anyway. Please calculate the minimum possible time required for that.


-----Input-----

The first line contains two integers $n$ and $m$ ($1 \le n \le 2 \cdot 10^5$; $1 \le m \le 10^9$) — the number of videos Monocarp wants to watch and the size of the hard disk, respectively.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le m$) — the sizes of the videos.


-----Output-----

Print one integer — the minimum time required to watch all $n$ videos.


-----Examples-----

Input
5 6
1 2 3 4 5
Output
16
Input
5 5
1 2 3 4 5
Output
17
Input
4 3
1 3 2 3
Output
12


-----Note-----

None

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Vova promised himself that he would never play computer games... But recently Firestorm — a well-known game developing company — published their newest game, World of Farcraft, and it became really popular. Of course, Vova started playing it.

Now he tries to solve a quest. The task is to come to a settlement named Overcity and spread a rumor in it.

Vova knows that there are n characters in Overcity. Some characters are friends to each other, and they share information they got. Also Vova knows that he can bribe each character so he or she starts spreading the rumor; i-th character wants c_{i} gold in exchange for spreading the rumor. When a character hears the rumor, he tells it to all his friends, and they start spreading the rumor to their friends (for free), and so on.

The quest is finished when all n characters know the rumor. What is the minimum amount of gold Vova needs to spend in order to finish the quest?

Take a look at the notes if you think you haven't understood the problem completely.


-----Input-----

The first line contains two integer numbers n and m (1 ≤ n ≤ 10^5, 0 ≤ m ≤ 10^5) — the number of characters in Overcity and the number of pairs of friends.

The second line contains n integer numbers c_{i} (0 ≤ c_{i} ≤ 10^9) — the amount of gold i-th character asks to start spreading the rumor.

Then m lines follow, each containing a pair of numbers (x_{i}, y_{i}) which represent that characters x_{i} and y_{i} are friends (1 ≤ x_{i}, y_{i} ≤ n, x_{i} ≠ y_{i}). It is guaranteed that each pair is listed at most once.


-----Output-----

Print one number — the minimum amount of gold Vova has to spend in order to finish the quest.


-----Examples-----
Input
5 2
2 5 3 4 8
1 4
4 5

Output
10

Input
10 0
1 2 3 4 5 6 7 8 9 10

Output
55

Input
10 5
1 6 2 7 3 8 4 9 5 10
1 2
3 4
5 6
7 8
9 10

Output
15



-----Note-----

In the first example the best decision is to bribe the first character (he will spread the rumor to fourth character, and the fourth one will spread it to fifth). Also Vova has to bribe the second and the third characters, so they know the rumor.

In the second example Vova has to bribe everyone.

In the third example the optimal decision is to bribe the first, the third, the fifth, the seventh and the ninth characters.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Chef has a calculator which has two screens and two buttons. Initially, each screen shows the number zero. Pressing the first button increments the number on the first screen by 1, and each click of the first button consumes 1 unit of energy.
Pressing the second button increases the number on the second screen by the number which is currently appearing on the first screen. Each click of the second button consumes B units of energy.
Initially the calculator has N units of energy.
Now chef wonders what the maximum possible number is, that he gets on the second screen of the calculator, with the limited energy.

-----Input-----
The first line of the input contains an integer T denoting the number of test cases.
Each test case is described using a single line containing two integers, N and B.

-----Output-----
For each test case, output a single line containing the answer to this test case.

-----Constraints-----
- 1 ≤ T ≤ 10,000
- 1 ≤ N, B ≤ 1,000,000,000

-----Subtasks-----
- Subtask 1 (20 points): 1 ≤ N, B ≤ 1,000
- Subtask 2 (80 points): Original constraints

-----Example-----
Input:
3
10 2
8 5
6 1

Output:
12
3
9

-----Explanation-----
Example case 1. There are 10 units of energy available. Pressing second button takes 2 units of energy. Chef can achieve 12 on the second screen as follows.

- Press first button to get scores (1, 0). 9 units of energey is left.
- Press first button to get scores (2, 0). 8 units of energy remaining.
- Press first button to get scores (3, 0). 7 units of energy remaining.
- Press first button to get scores (4, 0). 6 units of energy remaining.
- Press second button to get scores (4, 4). 4 units of energy remaining.
- Press second button to get scores (4, 8). 2 units of energy remaining.
- Press second button to get scores (4, 12). 0 units of energy remaining.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given n numbers a_1, a_2, ..., a_{n}. You can perform at most k operations. For each operation you can multiply one of the numbers by x. We want to make [Image] as large as possible, where $1$ denotes the bitwise OR. 

Find the maximum possible value of [Image] after performing at most k operations optimally.


-----Input-----

The first line contains three integers n, k and x (1 ≤ n ≤ 200 000, 1 ≤ k ≤ 10, 2 ≤ x ≤ 8).

The second line contains n integers a_1, a_2, ..., a_{n} (0 ≤ a_{i} ≤ 10^9).


-----Output-----

Output the maximum value of a bitwise OR of sequence elements after performing operations.


-----Examples-----
Input
3 1 2
1 1 1

Output
3

Input
4 2 3
1 2 4 8

Output
79



-----Note-----

For the first sample, any possible choice of doing one operation will result the same three numbers 1, 1, 2 so the result is $1|1|2 = 3$. 

For the second sample if we multiply 8 by 3 two times we'll get 72. In this case the numbers will become 1, 2, 4, 72 so the OR value will be 79 and is the largest possible result.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Finally, the pandemic is over in ChefLand, and the chef is visiting the school again. Chef likes to climb the stairs of his school's floor by skipping one step, sometimes chef climbs the stairs one by one. Simply, the chef can take one or 2 steps in one upward movement. There are N stairs between ground and next floor. The chef is on the ground floor and he wants to go to the next floor with Cheffina but, Cheffina asks chef in how many ways, the chef can reach the next floor normally or any combination of skipping one step, where order doesn't matter. 

-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow. 
- Each test case contains a single line of input, two integers $N$. 

-----Output:-----
For each test case, output in a single line answer as the number of ways.

-----Constraints-----
- $1 \leq T \leq 1000$
- $1 \leq N \leq 10^5$

-----Sample Input:-----
1
3

-----Sample Output:-----
2

-----EXPLANATION:-----
ways: [1,1,1], here chef climb to the next floor, one by one stair.
[1,2], here chef climb to the next floor, one step first and after that 2 stairs at once.
Note, [2,1] consider the same as that of [1,2] hence ignored.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
problem

Given the lengths of $ 2 $ sides that are not the hypotenuse of a right triangle, $ A $ and $ B $. The side of length $ A $ overlaps the $ x $ axis, and the side of length $ B $ overlaps the $ y $ axis.

Do the following:

1. Rotate the triangle around the $ x $ axis.
2. Rotate the shape created by performing the operation $ 1 $ around the $ y $ axis.



Perform the operation $ 2 $ to find the volume of the created figure.



output

Output the volume of the figure. Also, output a line break at the end. Absolute or relative errors less than $ 0.000001 $ are allowed.

Example

Input

1 2


Output

33.510322

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.