meetforever/GRPO_CL huggingface dataset:
user: There are N Snuke Cats numbered 1, 2, \ldots, N, where N is even.
Each Snuke Cat wears a red scarf, on which his favorite non-negative integer is written.
Recently, they learned the operation called xor (exclusive OR).What is xor?

For n non-negative integers x_1, x_2, \ldots, x_n, their xor, x_1~\textrm{xor}~x_2~\textrm{xor}~\ldots~\textrm{xor}~x_n is defined as follows:

 -  When x_1~\textrm{xor}~x_2~\textrm{xor}~\ldots~\textrm{xor}~x_n is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if the number of integers among x_1, x_2, \ldots, x_n whose binary representations have 1 in the 2^k's place is odd, and 0 if that count is even. 
For example, 3~\textrm{xor}~5 = 6.


They wanted to use this operation quickly, so each of them calculated the xor of the integers written on their scarfs except his scarf.
We know that the xor calculated by Snuke Cat i, that is, the xor of the integers written on the scarfs except the scarf of Snuke Cat i is a_i.
Using this information, restore the integer written on the scarf of each Snuke Cat.

-----Constraints-----
 - All values in input are integers.
 - 2 \leq N \leq 200000
 - N is even.
 - 0 \leq a_i \leq 10^9
 - There exists a combination of integers on the scarfs that is consistent with the given information.

-----Input-----
Input is given from Standard Input in the following format:
N
a_1 a_2 \ldots a_N

-----Output-----
Print a line containing N integers separated with space.
The i-th of the integers from the left should represent the integer written on the scarf of Snuke Cat i.
If there are multiple possible solutions, you may print any of them.

-----Sample Input-----
4
20 11 9 24

-----Sample Output-----
26 5 7 22

 - 5~\textrm{xor}~7~\textrm{xor}~22 = 20
 - 26~\textrm{xor}~7~\textrm{xor}~22 = 11
 - 26~\textrm{xor}~5~\textrm{xor}~22 = 9
 - 26~\textrm{xor}~5~\textrm{xor}~7 = 24
Thus, this output is consistent with the given information.
user: There is a tree with N vertices numbered 1 to N.
The i-th edge in this tree connects Vertex a_i and Vertex b_i, and the color and length of that edge are c_i and d_i, respectively.
Here the color of each edge is represented by an integer between 1 and N-1 (inclusive). The same integer corresponds to the same color, and different integers correspond to different colors.
Answer the following Q queries:
 - Query j (1 \leq j \leq Q): assuming that the length of every edge whose color is x_j is changed to y_j, find the distance between Vertex u_j and Vertex v_j. (The changes of the lengths of edges do not affect the subsequent queries.)

-----Constraints-----
 - 2 \leq N \leq 10^5
 - 1 \leq Q \leq 10^5
 - 1 \leq a_i, b_i \leq N
 - 1 \leq c_i \leq N-1
 - 1 \leq d_i \leq 10^4
 - 1 \leq x_j \leq N-1
 - 1 \leq y_j \leq 10^4
 - 1 \leq u_j < v_j \leq N
 - The given graph is a tree.
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N Q
a_1 b_1 c_1 d_1
:
a_{N-1} b_{N-1} c_{N-1} d_{N-1}
x_1 y_1 u_1 v_1
:
x_Q y_Q u_Q v_Q

-----Output-----
Print Q lines. The j-th line (1 \leq j \leq Q) should contain the answer to Query j.

-----Sample Input-----
5 3
1 2 1 10
1 3 2 20
2 4 4 30
5 2 1 40
1 100 1 4
1 100 1 5
3 1000 3 4

-----Sample Output-----
130
200
60

The graph in this input is as follows:

Here the edges of Color 1 are shown as solid red lines, the edge of Color 2 is shown as a bold green line, and the edge of Color 4 is shown as a blue dashed line.
 - Query 1: Assuming that the length of every edge whose color is 1 is changed to 100, the distance between Vertex 1 and Vertex 4 is 100 + 30 = 130.
 - Query 2: Assuming that the length of every edge whose color is 1 is changed to 100, the distance between Vertex 1 and Vertex 5 is 100 + 100 = 200.
 - Query 3: Assuming that the length of every edge whose color is 3 is changed to 1000 (there is no such edge), the distance between Vertex 3 and Vertex 4 is 20 + 10 + 30 = 60. Note that the edges of Color 1 now have their original lengths.
user: We have a tree with N vertices, whose i-th edge connects Vertex u_i and Vertex v_i.
Vertex i has an integer a_i written on it.
For every integer k from 1 through N, solve the following problem:
 - We will make a sequence by lining up the integers written on the vertices along the shortest path from Vertex 1 to Vertex k, in the order they appear. Find the length of the longest increasing subsequence of this sequence.
Here, the longest increasing subsequence of a sequence A of length L is the subsequence A_{i_1} , A_{i_2} , ... , A_{i_M} with the greatest possible value of M such that 1 \leq i_1 < i_2 < ... < i_M \leq L and A_{i_1} < A_{i_2} < ... < A_{i_M}.

-----Constraints-----
 - 2 \leq N \leq 2 \times 10^5
 - 1 \leq a_i \leq 10^9
 - 1 \leq u_i , v_i \leq N
 - u_i \neq v_i
 - The given graph is a tree.
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
u_1 v_1
u_2 v_2
:
u_{N-1} v_{N-1}

-----Output-----
Print N lines. The k-th line, print the length of the longest increasing subsequence of the sequence obtained from the shortest path from Vertex 1 to Vertex k.

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

-----Sample Output-----
1
2
3
3
4
4
5
2
2
3

For example, the sequence A obtained from the shortest path from Vertex 1 to Vertex 5 is 1,2,5,3,4. Its longest increasing subsequence is A_1, A_2, A_4, A_5, with the length of 4.
user: Write a program to take two numbers as input and print their difference if the first number is greater than the second number otherwise$otherwise$ print their sum.

-----Input:-----
- First line will contain the first number (N1$N1$)
- Second line will contain the second number (N2$N2$)

-----Output:-----
Output a single line containing the difference of 2 numbers (N1−N2)$(N1 - N2)$ if the first number is greater than the second number otherwise output their sum (N1+N2)$(N1 + N2)$.

-----Constraints-----
- −1000≤N1≤1000$-1000 \leq N1 \leq 1000$
- −1000≤N2≤1000$-1000 \leq N2 \leq 1000$

-----Sample Input:-----
82
28

-----Sample Output:-----
54
user: Witua is a little student from the University of Lviv. He enjoys studying math. Witua knows a lot of famous mathematicians like Eratosthenes, Pythagoras, Fermat, Diophantus, Furko, Gauss and so on. However, his favorite one is Euler. The only thing Witua likes more than Euler is Euler’s totient function φ. He is exploring the nature of this function. One of the steps of his work is finding φ(i)/i for all 2≤i≤N. He doesn’t need to know every such value, but Witua wonders for what value i, is φ(i)/i the maximum he can get? Help little student to find such i that φ(i)/i is maximum among all the  2≤i≤N.

-----Input-----
The first line contains single integer T - the number of test cases. Each of the next T lines contains a single integer N. 

-----Output-----
For every test case output i such that φ(i)/i is maximum among all i (2≤i≤N) in a separate line.

-----Constrains-----
T (1≤T≤500 )

N(2≤N≤10^18)


-----Example-----
Input:
3
2
3
4

Output:
2
3
3

Explanationφ(2)/2=1/2
φ(3)/3=2/3
φ(4)/4=2/4
user: Almir had a small sequence $A_1, A_2, \ldots, A_N$. He decided to make $K$ copies of this sequence and concatenate them, forming a sequence $X_1, X_2, \ldots, X_{NK}$; for each valid $i$ and $j$ ($0 \le j < K$), $X_{j \cdot N + i} = A_i$.
For example, if $A = (1, 2, 3)$ and $K = 4$, the final sequence is $X = (1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3)$.
A pair $(i, j)$, where $1 \le i < j \le N$, is an inversion if $X_i > X_j$. Find the number of inversions in the final sequence $X$.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains two space-separated integers $N$ and $K$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Output-----
For each test case, print a single line containing one integer ― the number of inversions in the sequence $X$.

-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N \le 100$
- $1 \le K \le 10^6$
- $1 \le A_i \le 10^9$ for each valid $i$

-----Subtasks-----
Subtask #1 (100 points): original constraints

-----Example Input-----
2
3 3
2 1 3
4 100
99 2 1000 24

-----Example Output-----
12
30000
user: Indian National Olympiad in Informatics 2015
A string is any nonempty sequence of 0s and 1s. Examples of strings are 00, 101, 111000, 1, 0, 01. The length of a string is the number of symbols in it. For example, the length of 111000 is 6. If u and v are strings, then uv is the string obtained by concatenating u and v. For example if u = 110 and v = 0010 then uv = 1100010.
A string w is periodic if there exists a string v such that w = vn = vv · · · v (n times), for some n ≥ 2. Note that in this case the length of v is strictly less than that of w. For example, 110110 is periodic, because it is vv for v = 110.
Given a positive integer N , find the number of strings of length N which are not periodic. Report the answer modulo M . The non-periodic strings of length 2 are 10 and 01. The non- periodic strings of length 3 are 001, 010, 011, 100, 101, and 110.

-----Input format-----
A single line, with two space-separated integers, N and M .

-----Output format-----
A single integer, the number of non-periodic strings of length N , modulo M .

-----Test Data-----
In all subtasks, 2 ≤ M ≤ 108. The testdata is grouped into 4 subtasks.
Subtask 1 (10 marks) 1 ≤ N ≤ 4000. N is the product of two distinct prime numbers.
Subtask 2 (20 marks) 1 ≤ N ≤ 4000. N is a power of a prime number.
Subtask 3 (35 marks) 1 ≤ N ≤ 4000.
Subtask 4 (35 marks) 1 ≤ N ≤ 150000.

-----Example-----
Here is the sample input and output corresponding to the example above:

-----Sample input-----
3 176

-----Sample output-----
6

Note: Your program should not print anything other than what is specified in the output format. Please remove all diagnostic print statements before making your final submission. A program with extraneous output will be treated as incorrect!
user: 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.
user: Write a program that takes in a letterclass ID of a ship and display the equivalent string class description of the given ID. Use the table below.

Class ID Ship ClassB or bBattleShipC or cCruiserD or dDestroyerF or fFrigate

-----Input-----

The first line contains an integer T, the total number of testcases. Then T lines follow, each line contains a character. 

-----Output-----
For each test case, display the Ship Class depending on ID, in a new line.

-----Constraints-----
- 1 ≤ T ≤ 1000

-----Example-----
Input

3 
B
c
D

Output
BattleShip
Cruiser
Destroyer
user: Nature photographing may be fun for tourists, but it is one of the most complicated things for photographers. To capture all the facets of a bird, you might need more than one cameras. You recently encountered such a situation.
There are $n$ photographers, so there are $n$ cameras in a line on the x-axis. All the cameras are at distinct coordinates. 
You want to pair up these cameras ($n$ is even) in such a way that the sum of angles subtended on the bird by the pair of cameras is maximized. Formally, let A, B be two cameras, and let P be the bird to be captured by these two cameras. The angle will APB. 
Note: All angles are in radians.

-----Input-----
- The first line of the input contains an integer $T$ denoting the number of test cases. The description of the test cases follows.
- The first line of each test case contains an integer $n$.
- The second line of each test case contains $n$ space-separated integers denoting the $x_i$ coordinates of the cameras.
- The third line of each test case contains two space-separated integers $P, Q$ denoting the x and y coordinates of the bird respectively.

-----Output-----
For each test case, output your answer in a single line. Your answer would be considered correct if its absolute error is less than or equal to 1e-6 of the actual answer. 

-----Constraints-----
- $1 \le T \le 10$
- $2 \le n \leq  100$
- $1 \le x_i \leq 300$
- $0 \le P \leq 300$
- $1 \le Q \leq 300$

-----Example Input-----
2
2
0 1
0 1
2
0 1
100 1

-----Example Output-----
0.785398163397
0.000100999899

-----Explanation-----
Note: $1 \leq x_i$ is not being satisfied by the sample input, but will be satisfied in the actual test data.
Testcase 1: There are only 2 cameras, so they have to paired up with each other. And the angle subtended by then is 45 degrees. Converting this to radians gives the output.
user: Three Best Friends $AMAN$ , $AKBAR$ , $ANTHONY$ are planning to go to “GOA”  , but just like every other goa trip plan there is a problem to their plan too.
Their parents will only give permission if they can solve this problem for them
They are a given a number N and they have to calculate the total number of triplets (x ,y ,z)
Satisfying the given condition  y * x +z=n.
For ex if N=3
Then there exist 3 triplets( x ,y ,z):   (1,1,2) , (1,2,1) , (2,1,1) which satisfy the condition
Help the group to get permission for the trip

-----Input:-----
- First line will contain the number  $N$.

-----Output:-----
the possible number of triplets satisfying the given condition

-----Constraints-----
- $2 \leq N \leq 10^6$

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

-----Sample Output:-----
3

-----EXPLANATION:-----
there exist 3 triplets ( x ,y ,z):   (1,1,2) , (1,2,1) , (2,1,1)  which satisfy the condition
user: Maheshmati and Sangu are playing a game. First, Maheshmati gives Sangu a sequence of $N$ distinct integers $a_1, a_2, \dots, a_N$ (not necessarily sorted) and an integer $K$. Sangu has to create all subsequences of this sequence with length $K$. For each subsequence, he has to write down the product of $K-2$ integers: all elements of this subsequence except the minimum and maximum element.
Sangu wins the game if he is able to write down all these numbers and tell Maheshmati their product (modulo $10^9+7$, since it can be very large). However, Sangu is a very lazy child and thus wants you to help him win this game. Compute the number Sangu should tell Maheshmati!

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains two space-separated integers $N$ and $K$.
- The second line contains $N$ space-separated integers $a_1, a_2, \dots, a_N$.

-----Output-----
For each test case, print a single line containing one integer — the product of all numbers written down by Sangu modulo $10^9+7$.

-----Constraints-----
- $1 \le T \le 10$
- $3 \le N \le 5,000$
- $3 \le K \le N$
- $1 \le a_i \le 10,000$ for each valid $i$
- the numbers $a_1, a_2, \dots, a_N$ are pairwise distinct

-----Subtasks-----
Subtask #1 (20 points): $1 \le N \le 10$
Subtask #2 (80 points): original constraints

-----Example Input-----
1
4 3 
1 2 3 4 

-----Example Output-----
36

-----Explanation-----
Example case 1: There are four possible subsequences:
- $[1, 2, 3]$ (Sangu should write down $2$.)
- $[1, 3, 4]$ (Sangu should write down $3$.)
- $[1, 2, 4]$ (Sangu should write down $2$.)
- $[2, 3, 4]$ (Sangu should write down $3$.)
The required product is $2 \cdot 3 \cdot 2 \cdot 3 = 36$.
user: There are total $N$ cars in a sequence with $ith$ car being assigned with an alphabet equivalent to the $ith$ alphabet of string $S$ . Chef has been assigned a task to calculate the total number of cars with alphabet having a unique even value in the given range X to Y (both inclusive)
. The value of an alphabet is simply its position in alphabetical order e.g.: a=1, b=2, c=3…
The chef will be given $Q$
such tasks having varying values of $X$ and $Y$
Note: string $S$ contains only lowercase alphabets

-----Input-----
First line of input contains a string $S$ of length $N$.
Second line contains an integer denoting no. of queries $Q$.
Next q lines contain two integers denoting values of $X$ and $Y$.

-----Output-----
For each query print a single integer denoting total number of cars with alphabet having a unique even value in the given range $X$ to $Y$.

-----Constraints-----
- $1 \leq n \leq 10^5$
- $1 \leq q \leq 10^5$

-----Example Input-----
bbccdd
5
1 2
3 4
5 6
1 6
2 5

-----Example Output-----
1
0
1
2
2

-----Explanation:-----
Example case 1: 
Query 1: range 1 to 2 contains the substring $"bb"$ where each character has a value of 2. Since we will only be considering unique even values, the output will be 1
user: You are given three numbers $a$, $b$, $c$ . Write a program to determine the largest number that is less than or equal to $c$ and leaves a remainder $b$ when divided by $a$.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- Each testcase contains a single line of input, having three integers $a$, $b$, $c$.

-----Output:-----
- For each testcase, output in a single line the largest number less than or equal to $c$.

-----Constraints:-----
- $1 \leq T  \leq 100000$
- $0 \leq b < a < c \leq$ $10$^18

-----Sample Input:-----
1
7 2 10

-----Sample Output:-----
9
user: Aureole the Techno-cultural fest of JEC thought of conducting a workshop on big data, as the topic is hot everyone wants to take part but due to limited seats in the Jashan Auditorium there is a selection criteria, a problem is given.
the problem states a string is to be compressed when two or more consecutive characters are same they are to be compressed into one character and the original number count is to be written after it ex. aaabb -> a3b2
where every character is of 8bits and every integer is of 32bits
you are asked to find the difference in size between original string and compressed string

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains of a single line of input $S$ the string to be compressed. 

-----Output:-----
For each testcase, output in a single line The difference in size.

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq |S| \leq 10^5$

-----Subtasks-----
- 40 points : S will contain only a-z
- 60 points : S will contain 0-9 characters also

-----Sample Input:-----
1
aaabb

-----Sample Output:-----
-40

-----EXPLANATION:-----
the resulting string will be a3b2 its size will be 80, original string size will be 40 so ans= 40-80
user: Given an Array of length  $N$  containing elements $Ai$ ( i = 1 to n ) . You have to handle $Q$ queries on this array . Each Query is of two types k=(1 or 2). 
Type 1:- $k$ $l$ $r$ in which you have to tell whether the product of numbers in range l to r results in a perfect square or not. if product of numbers in range $l$ to$r$ is a perfect square then simply output YES else output NO.
Type 2:- $k$ $i$ $val$ Multiply the value present at index $i$ with $val$.
Note#1: 1 based indexing in each query.
Note#2: Values of prime factors of all numbers $val$ and $Ai$ is between 2 to 100 only.

-----Input:-----
- First line will contain $N$, denoting the size of the array. Then the next line follow. 
- N integers  $Ai - An$.
- Third line will contain $Q$, denoting the number of queries. Then the next $Q$ lines follow -description of each query. 
- Each query consists of either type 1 or type 2 and each query gives you three elements either
-{$k$ $l$ $r$} or {$k$ $i$ $val$}

-----Output:-----
For each  Query of Type 1 Output either "YES" or "NO" Without Quotes.

-----Constraints-----
- $1 \leq N \leq 20000$
- $1 \leq Q \leq 20000$
- $2 \leq Ai \leq 1000000$
- $1 \leq i ,l,r \leq N$
- $1 \leq val \leq 1000000$
- $1 \leq l \leq r$

-----Subtasks-----
Subtask 1 :-40 points 
- Values of prime factors of all numbers $val$ and $Ai$ is between 2 to 40 only.
Subtask 2 :- 60 points
- Original Constraints 

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

-----Sample Output:-----
YES
NO
YES

-----EXPLANATION:-----
-Query 1 :- product of numbers in range 1 to 2=2 * 2=4 (perfect square so YES)
-Query 2:- product of numbers in range 3 to 4 = 3 * 4 = 12 (not perfect square so NO)
-Query 3:- multiply number at index3 with 3 so number at index 3= 3*3 = 9 .
-Query 4:- product of numbers in range 1 to 4 = 2 * 2 * 9 * 4 = 144 (perfect square so YES)
user: Recently in JEC ants have become huge, the Principal is on a journey to snipe them !!
Principal has limited $N$ practice Bullets to practice so that he can be sure to kill ants.
- The Practice ground has max length $L$.
- There is a Limit X such that if the bullet is fired beyond this, it will destroy and it wont be of any further use.
- Bullet can be reused if fired in a range strictly less than X.
He wants to find minimum number of shots taken to find  the distance X by using $N$ bullets.

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

-----Output:-----
For each testcase, output in a single line answer the minimum number of shots to find the distance X.

-----Constraints-----
- $1 \leq T \leq 10$
- $2 \leq N,L \leq 100$
*N is always less than  equal to square root of L

-----Subtasks-----
- 10 points : $ N = 1$
- 40 points : $ N = 2$
- 50 points : Original Constraints.

-----Sample Input:-----
2
1 10
2 10

-----Sample Output:-----
10
4

-----EXPLANATION:-----
- 
There is only single bullet which is to be fired from distance 1 to 10 to get the distance X so in the worst case it can take up to 10 shots to find the distance X.
- 
there are 2 bullets and distance 10 meters suppose if distance X is 10 we can get to that by firing first bullet at 4 then 7 then 9 then  at 10 it will break  it took only 4 turns, and if the distance X was 3, we can get that by firing first bullet at 4 it will get destroyed than we use 2nd bullet at 1 , 2, 3  and 2nd bullet will also break it also took 4 turns. You can check for any position minimum number of turns will be at most 4.
user: Given an integer N. Integers A and B are chosen randomly in the range [1..N]. Calculate the probability that the Greatest Common Divisor(GCD) of A and B equals to B.

-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows. Each test case consists of a single integer N on a separate line.

-----Output-----
For each test case, output a single line containing probability as an irreducible fraction. 

-----Example-----
Input:
3
1
2
3

Output:
1/1
3/4
5/9

-----Constraints-----

1<=T<=103

1<=N<=109