meetforever/GRPO_CL huggingface dataset:
user: You are given two strings $s$ and $t$, both consisting of exactly $k$ lowercase Latin letters, $s$ is lexicographically less than $t$.

Let's consider list of all strings consisting of exactly $k$ lowercase Latin letters, lexicographically not less than $s$ and not greater than $t$ (including $s$ and $t$) in lexicographical order. For example, for $k=2$, $s=$"az" and $t=$"bf" the list will be ["az", "ba", "bb", "bc", "bd", "be", "bf"].

Your task is to print the median (the middle element) of this list. For the example above this will be "bc".

It is guaranteed that there is an odd number of strings lexicographically not less than $s$ and not greater than $t$.


-----Input-----

The first line of the input contains one integer $k$ ($1 \le k \le 2 \cdot 10^5$) — the length of strings.

The second line of the input contains one string $s$ consisting of exactly $k$ lowercase Latin letters.

The third line of the input contains one string $t$ consisting of exactly $k$ lowercase Latin letters.

It is guaranteed that $s$ is lexicographically less than $t$.

It is guaranteed that there is an odd number of strings lexicographically not less than $s$ and not greater than $t$.


-----Output-----

Print one string consisting exactly of $k$ lowercase Latin letters — the median (the middle element) of list of strings of length $k$ lexicographically not less than $s$ and not greater than $t$.


-----Examples-----
Input
2
az
bf

Output
bc

Input
5
afogk
asdji

Output
alvuw

Input
6
nijfvj
tvqhwp

Output
qoztvz
user: There are $n$ students in a school class, the rating of the $i$-th student on Codehorses is $a_i$. You have to form a team consisting of $k$ students ($1 \le k \le n$) such that the ratings of all team members are distinct.

If it is impossible to form a suitable team, print "NO" (without quotes). Otherwise print "YES", and then print $k$ distinct numbers which should be the indices of students in the team you form. If there are multiple answers, print any of them.


-----Input-----

The first line contains two integers $n$ and $k$ ($1 \le k \le n \le 100$) — the number of students and the size of the team you have to form.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 100$), where $a_i$ is the rating of $i$-th student.


-----Output-----

If it is impossible to form a suitable team, print "NO" (without quotes). Otherwise print "YES", and then print $k$ distinct integers from $1$ to $n$ which should be the indices of students in the team you form. All the ratings of the students in the team should be distinct. You may print the indices in any order. If there are multiple answers, print any of them.

Assume that the students are numbered from $1$ to $n$.


-----Examples-----
Input
5 3
15 13 15 15 12

Output
YES
1 2 5 

Input
5 4
15 13 15 15 12

Output
NO

Input
4 4
20 10 40 30

Output
YES
1 2 3 4 



-----Note-----

All possible answers for the first example:   {1 2 5}  {2 3 5}  {2 4 5} 

Note that the order does not matter.
user: Two integer sequences existed initially, one of them was strictly increasing, and another one — strictly decreasing.

Strictly increasing sequence is a sequence of integers $[x_1 < x_2 < \dots < x_k]$. And strictly decreasing sequence is a sequence of integers $[y_1 > y_2 > \dots > y_l]$. Note that the empty sequence and the sequence consisting of one element can be considered as increasing or decreasing.

Elements of increasing sequence were inserted between elements of the decreasing one (and, possibly, before its first element and after its last element) without changing the order. For example, sequences $[1, 3, 4]$ and $[10, 4, 2]$ can produce the following resulting sequences: $[10, \textbf{1}, \textbf{3}, 4, 2, \textbf{4}]$, $[\textbf{1}, \textbf{3}, \textbf{4}, 10, 4, 2]$. The following sequence cannot be the result of these insertions: $[\textbf{1}, 10, \textbf{4}, 4, \textbf{3}, 2]$ because the order of elements in the increasing sequence was changed.

Let the obtained sequence be $a$. This sequence $a$ is given in the input. Your task is to find any two suitable initial sequences. One of them should be strictly increasing, and another one — strictly decreasing. Note that the empty sequence and the sequence consisting of one element can be considered as increasing or decreasing.

If there is a contradiction in the input and it is impossible to split the given sequence $a$ into one increasing sequence and one decreasing sequence, print "NO".


-----Input-----

The first line of the input contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of elements in $a$.

The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2 \cdot 10^5$), where $a_i$ is the $i$-th element of $a$.


-----Output-----

If there is a contradiction in the input and it is impossible to split the given sequence $a$ into one increasing sequence and one decreasing sequence, print "NO" in the first line.

Otherwise print "YES" in the first line. In the second line, print a sequence of $n$ integers $res_1, res_2, \dots, res_n$, where $res_i$ should be either $0$ or $1$ for each $i$ from $1$ to $n$. The $i$-th element of this sequence should be $0$ if the $i$-th element of $a$ belongs to the increasing sequence, and $1$ otherwise. Note that the empty sequence and the sequence consisting of one element can be considered as increasing or decreasing.


-----Examples-----
Input
9
5 1 3 6 8 2 9 0 10

Output
YES
1 0 0 0 0 1 0 1 0 

Input
5
1 2 4 0 2

Output
NO
user: Vova plans to go to the conference by train. Initially, the train is at the point $1$ and the destination point of the path is the point $L$. The speed of the train is $1$ length unit per minute (i.e. at the first minute the train is at the point $1$, at the second minute — at the point $2$ and so on).

There are lanterns on the path. They are placed at the points with coordinates divisible by $v$ (i.e. the first lantern is at the point $v$, the second is at the point $2v$ and so on).

There is also exactly one standing train which occupies all the points from $l$ to $r$ inclusive.

Vova can see the lantern at the point $p$ if $p$ is divisible by $v$ and there is no standing train at this position ($p \not\in [l; r]$). Thus, if the point with the lantern is one of the points covered by the standing train, Vova can't see this lantern.

Your problem is to say the number of lanterns Vova will see during the path. Vova plans to go to $t$ different conferences, so you should answer $t$ independent queries.


-----Input-----

The first line of the input contains one integer $t$ ($1 \le t \le 10^4$) — the number of queries.

Then $t$ lines follow. The $i$-th line contains four integers $L_i, v_i, l_i, r_i$ ($1 \le L, v \le 10^9$, $1 \le l \le r \le L$) — destination point of the $i$-th path, the period of the lantern appearance and the segment occupied by the standing train.


-----Output-----

Print $t$ lines. The $i$-th line should contain one integer — the answer for the $i$-th query.


-----Example-----
Input
4
10 2 3 7
100 51 51 51
1234 1 100 199
1000000000 1 1 1000000000

Output
3
0
1134
0



-----Note-----

For the first example query, the answer is $3$. There are lanterns at positions $2$, $4$, $6$, $8$ and $10$, but Vova didn't see the lanterns at positions $4$ and $6$ because of the standing train.

For the second example query, the answer is $0$ because the only lantern is at the point $51$ and there is also a standing train at this point.

For the third example query, the answer is $1134$ because there are $1234$ lanterns, but Vova didn't see the lanterns from the position $100$ to the position $199$ inclusive.

For the fourth example query, the answer is $0$ because the standing train covers the whole path.
user: One day, $n$ people ($n$ is an even number) met on a plaza and made two round dances, each round dance consists of exactly $\frac{n}{2}$ people. Your task is to find the number of ways $n$ people can make two round dances if each round dance consists of exactly $\frac{n}{2}$ people. Each person should belong to exactly one of these two round dances.

Round dance is a dance circle consisting of $1$ or more people. Two round dances are indistinguishable (equal) if one can be transformed to another by choosing the first participant. For example, round dances $[1, 3, 4, 2]$, $[4, 2, 1, 3]$ and $[2, 1, 3, 4]$ are indistinguishable.

For example, if $n=2$ then the number of ways is $1$: one round dance consists of the first person and the second one of the second person.

For example, if $n=4$ then the number of ways is $3$. Possible options:  one round dance — $[1,2]$, another — $[3,4]$;  one round dance — $[2,4]$, another — $[3,1]$;  one round dance — $[4,1]$, another — $[3,2]$. 

Your task is to find the number of ways $n$ people can make two round dances if each round dance consists of exactly $\frac{n}{2}$ people.


-----Input-----

The input contains one integer $n$ ($2 \le n \le 20$), $n$ is an even number.


-----Output-----

Print one integer — the number of ways to make two round dances. It is guaranteed that the answer fits in the $64$-bit integer data type.


-----Examples-----
Input
2

Output
1

Input
4

Output
3

Input
8

Output
1260

Input
20

Output
12164510040883200
user: You are given a string $s$ consisting of $n$ lowercase Latin letters. Polycarp wants to remove exactly $k$ characters ($k \le n$) from the string $s$. Polycarp uses the following algorithm $k$ times:

  if there is at least one letter 'a', remove the leftmost occurrence and stop the algorithm, otherwise go to next item;  if there is at least one letter 'b', remove the leftmost occurrence and stop the algorithm, otherwise go to next item;  ...  remove the leftmost occurrence of the letter 'z' and stop the algorithm. 

This algorithm removes a single letter from the string. Polycarp performs this algorithm exactly $k$ times, thus removing exactly $k$ characters.

Help Polycarp find the resulting string.


-----Input-----

The first line of input contains two integers $n$ and $k$ ($1 \le k \le n \le 4 \cdot 10^5$) — the length of the string and the number of letters Polycarp will remove.

The second line contains the string $s$ consisting of $n$ lowercase Latin letters.


-----Output-----

Print the string that will be obtained from $s$ after Polycarp removes exactly $k$ letters using the above algorithm $k$ times.

If the resulting string is empty, print nothing. It is allowed to print nothing or an empty line (line break).


-----Examples-----
Input
15 3
cccaabababaccbc

Output
cccbbabaccbc

Input
15 9
cccaabababaccbc

Output
cccccc

Input
1 1
u

Output
user: The only difference between easy and hard versions is constraints.

Ivan plays a computer game that contains some microtransactions to make characters look cooler. Since Ivan wants his character to be really cool, he wants to use some of these microtransactions — and he won't start playing until he gets all of them.

Each day (during the morning) Ivan earns exactly one burle.

There are $n$ types of microtransactions in the game. Each microtransaction costs $2$ burles usually and $1$ burle if it is on sale. Ivan has to order exactly $k_i$ microtransactions of the $i$-th type (he orders microtransactions during the evening).

Ivan can order any (possibly zero) number of microtransactions of any types during any day (of course, if he has enough money to do it). If the microtransaction he wants to order is on sale then he can buy it for $1$ burle and otherwise he can buy it for $2$ burles.

There are also $m$ special offers in the game shop. The $j$-th offer $(d_j, t_j)$ means that microtransactions of the $t_j$-th type are on sale during the $d_j$-th day.

Ivan wants to order all microtransactions as soon as possible. Your task is to calculate the minimum day when he can buy all microtransactions he want and actually start playing.


-----Input-----

The first line of the input contains two integers $n$ and $m$ ($1 \le n, m \le 2 \cdot 10^5$) — the number of types of microtransactions and the number of special offers in the game shop.

The second line of the input contains $n$ integers $k_1, k_2, \dots, k_n$ ($0 \le k_i \le 2 \cdot 10^5$), where $k_i$ is the number of copies of microtransaction of the $i$-th type Ivan has to order. It is guaranteed that sum of all $k_i$ is not less than $1$ and not greater than $2 \cdot 10^5$.

The next $m$ lines contain special offers. The $j$-th of these lines contains the $j$-th special offer. It is given as a pair of integers $(d_j, t_j)$ ($1 \le d_j \le 2 \cdot 10^5, 1 \le t_j \le n$) and means that microtransactions of the $t_j$-th type are on sale during the $d_j$-th day.


-----Output-----

Print one integer — the minimum day when Ivan can order all microtransactions he wants and actually start playing.


-----Examples-----
Input
5 6
1 2 0 2 0
2 4
3 3
1 5
1 2
1 5
2 3

Output
8

Input
5 3
4 2 1 3 2
3 5
4 2
2 5

Output
20
user: A star is a figure of the following type: an asterisk character '*' in the center of the figure and four rays (to the left, right, top, bottom) of the same positive length. The size of a star is the length of its rays. The size of a star must be a positive number (i.e. rays of length $0$ are not allowed).

Let's consider empty cells are denoted by '.', then the following figures are stars:

 [Image] The leftmost figure is a star of size $1$, the middle figure is a star of size $2$ and the rightmost figure is a star of size $3$. 

You are given a rectangular grid of size $n \times m$ consisting only of asterisks '*' and periods (dots) '.'. Rows are numbered from $1$ to $n$, columns are numbered from $1$ to $m$. Your task is to draw this grid using any number of stars or find out that it is impossible. Stars can intersect, overlap or even coincide with each other. The number of stars in the output can't exceed $n \cdot m$. Each star should be completely inside the grid. You can use stars of same and arbitrary sizes.

In this problem, you do not need to minimize the number of stars. Just find any way to draw the given grid with at most $n \cdot m$ stars.


-----Input-----

The first line of the input contains two integers $n$ and $m$ ($3 \le n, m \le 1000$) — the sizes of the given grid.

The next $n$ lines contains $m$ characters each, the $i$-th line describes the $i$-th row of the grid. It is guaranteed that grid consists of characters '*' and '.' only.


-----Output-----

If it is impossible to draw the given grid using stars only, print "-1".

Otherwise in the first line print one integer $k$ ($0 \le k \le n \cdot m$) — the number of stars needed to draw the given grid. The next $k$ lines should contain three integers each — $x_j$, $y_j$ and $s_j$, where $x_j$ is the row index of the central star character, $y_j$ is the column index of the central star character and $s_j$ is the size of the star. Each star should be completely inside the grid.


-----Examples-----
Input
6 8
....*...
...**...
..*****.
...**...
....*...
........

Output
3
3 4 1
3 5 2
3 5 1

Input
5 5
.*...
****.
.****
..**.
.....

Output
3
2 2 1
3 3 1
3 4 1

Input
5 5
.*...
***..
.*...
.*...
.....

Output
-1

Input
3 3
*.*
.*.
*.*

Output
-1



-----Note-----

In the first example the output 2

3 4 1

3 5 2



is also correct.
user: You are given a three-digit positive integer N.

Determine whether N is a palindromic number.

Here, a palindromic number is an integer that reads the same backward as forward in decimal notation.

-----Constraints-----
 - 100≤N≤999
 - N is an integer.

-----Input-----
Input is given from Standard Input in the following format:  
N

-----Output-----
If N is a palindromic number, print Yes; otherwise, print No.

-----Sample Input-----
575

-----Sample Output-----
Yes

N=575 is also 575 when read backward, so it is a palindromic number. You should print Yes.
user: Alice and Bob are playing One Card Poker.

One Card Poker is a two-player game using playing cards.  
Each card in this game shows an integer between 1 and 13, inclusive.

The strength of a card is determined by the number written on it, as follows:  
Weak 2 < 3 < 4 < 5 < 6 < 7 < 8 < 9 < 10 < 11 < 12 < 13 < 1 Strong  
One Card Poker is played as follows:  
 - Each player picks one card from the deck. The chosen card becomes the player's hand.
 - The players reveal their hands to each other. The player with the stronger card wins the game.
If their cards are equally strong, the game is drawn.  
You are watching Alice and Bob playing the game, and can see their hands.

The number written on Alice's card is A, and the number written on Bob's card is B.

Write a program to determine the outcome of the game.  

-----Constraints-----
 - 1≦A≦13 
 - 1≦B≦13 
 - A and B are integers.

-----Input-----
The input is given from Standard Input in the following format:
A B

-----Output-----
Print Alice if Alice will win. Print Bob if Bob will win. Print Draw if the game will be drawn.

-----Sample Input-----
8 6

-----Sample Output-----
Alice

8 is written on Alice's card, and 6 is written on Bob's card.
Alice has the stronger card, and thus the output should be Alice.
user: As a New Year's gift, Dolphin received a string s of length 19.

The string s has the following format: [five lowercase English letters],[seven lowercase English letters],[five lowercase English letters].

Dolphin wants to convert the comma-separated string s into a space-separated string.

Write a program to perform the conversion for him.  

-----Constraints-----
 - The length of s is 19.
 - The sixth and fourteenth characters in s are ,.
 - The other characters in s are lowercase English letters.

-----Input-----
The input is given from Standard Input in the following format:
s

-----Output-----
Print the string after the conversion.

-----Sample Input-----
happy,newyear,enjoy

-----Sample Output-----
happy newyear enjoy

Replace all the commas in happy,newyear,enjoy with spaces to obtain happy newyear enjoy.
user: There are N students and M checkpoints on the xy-plane.

The coordinates of the i-th student (1 \leq i \leq N) is (a_i,b_i), and the coordinates of the checkpoint numbered j (1 \leq j \leq M) is (c_j,d_j).

When the teacher gives a signal, each student has to go to the nearest checkpoint measured in Manhattan distance. 

The Manhattan distance between two points (x_1,y_1) and (x_2,y_2) is |x_1-x_2|+|y_1-y_2|.

Here, |x| denotes the absolute value of x.

If there are multiple nearest checkpoints for a student, he/she will select the checkpoint with the smallest index.

Which checkpoint will each student go to?

-----Constraints-----
 - 1 \leq N,M \leq 50
 - -10^8 \leq a_i,b_i,c_j,d_j \leq 10^8
 - All input values are integers.

-----Input-----
The input is given from Standard Input in the following format:
N M
a_1 b_1
:  
a_N b_N
c_1 d_1
:  
c_M d_M

-----Output-----
Print N lines.

The i-th line (1 \leq i \leq N) should contain the index of the checkpoint for the i-th student to go.

-----Sample Input-----
2 2
2 0
0 0
-1 0
1 0

-----Sample Output-----
2
1

The Manhattan distance between the first student and each checkpoint is:
 - For checkpoint 1: |2-(-1)|+|0-0|=3
 - For checkpoint 2: |2-1|+|0-0|=1
The nearest checkpoint is checkpoint 2. Thus, the first line in the output should contain 2.
The Manhattan distance between the second student and each checkpoint is:
 - For checkpoint 1: |0-(-1)|+|0-0|=1
 - For checkpoint 2: |0-1|+|0-0|=1
When there are multiple nearest checkpoints, the student will go to the checkpoint with the smallest index. Thus, the second line in the output should contain 1.
user: Given an integer a as input, print the value a + a^2 + a^3.

-----Constraints-----
 - 1 \leq a \leq 10
 - a is an integer.

-----Input-----
Input is given from Standard Input in the following format:
a

-----Output-----
Print the value a + a^2 + a^3 as an integer.

-----Sample Input-----
2

-----Sample Output-----
14

When a = 2, we have a + a^2 + a^3 = 2 + 2^2 + 2^3 = 2 + 4 + 8 = 14.
Print the answer as an input. Outputs such as 14.0 will be judged as incorrect.
user: You are given an image A composed of N rows and N columns of pixels, and a template image B composed of M rows and M columns of pixels.

A pixel is the smallest element of an image, and in this problem it is a square of size 1×1.

Also, the given images are binary images, and the color of each pixel is either white or black.  
In the input, every pixel is represented by a character: . corresponds to a white pixel, and # corresponds to a black pixel.

The image A is given as N strings A_1,...,A_N.

The j-th character in the string A_i corresponds to the pixel at the i-th row and j-th column of the image A (1≦i,j≦N).

Similarly, the template image B is given as M strings B_1,...,B_M.

The j-th character in the string B_i corresponds to the pixel at the i-th row and j-th column of the template image B (1≦i,j≦M).  
Determine whether the template image B is contained in the image A when only parallel shifts can be applied to the images.  

-----Constraints-----
 - 1≦M≦N≦50 
 - A_i is a string of length N consisting of # and ..
 - B_i is a string of length M consisting of # and ..

-----Input-----
The input is given from Standard Input in the following format:
N M
A_1
A_2
:  
A_N
B_1
B_2
:  
B_M

-----Output-----
Print Yes if the template image B is contained in the image A. Print No otherwise.

-----Sample Input-----
3 2
#.#
.#.
#.#
#.
.#

-----Sample Output-----
Yes

The template image B is identical to the upper-left 2 × 2 subimage and the lower-right 2 × 2 subimage of A. Thus, the output should be Yes.
user: You have decided to give an allowance to your child depending on the outcome of the game that he will play now.
The game is played as follows:
 - There are three "integer panels", each with a digit between 1 and 9 (inclusive) printed on it, and one "operator panel" with a + printed on it.
 - The player should construct a formula of the form X + Y, by arranging the four panels from left to right. (The operator panel should not be placed at either end of the formula.)
 - Then, the amount of the allowance will be equal to the resulting value of the formula.
Given the values A, B and C printed on the integer panels used in the game, find the maximum possible amount of the allowance.

-----Constraints-----
 - All values in input are integers.
 - 1 \leq A, B, C \leq 9

-----Input-----
Input is given from Standard Input in the following format:
A B C

-----Output-----
Print the maximum possible amount of the allowance.

-----Sample Input-----
1 5 2

-----Sample Output-----
53

The amount of the allowance will be 53 when the panels are arranged as 52+1, and this is the maximum possible amount.
user: In some other world, today is the day before Christmas Eve.
Mr. Takaha is buying N items at a department store. The regular price of the i-th item (1 \leq i \leq N) is p_i yen (the currency of Japan).
He has a discount coupon, and can buy one item with the highest price for half the regular price. The remaining N-1 items cost their regular prices. What is the total amount he will pay?

-----Constraints-----
 - 2 \leq N \leq 10
 - 100 \leq p_i \leq 10000
 - p_i is an even number.

-----Input-----
Input is given from Standard Input in the following format:
N
p_1
p_2
:
p_N

-----Output-----
Print the total amount Mr. Takaha will pay.

-----Sample Input-----
3
4980
7980
6980

-----Sample Output-----
15950

The 7980-yen item gets the discount and the total is 4980 + 7980 / 2 + 6980 = 15950 yen.
Note that outputs such as 15950.0 will be judged as Wrong Answer.