meetforever/GRPO_CL huggingface dataset:
user: Watson gives to Sherlock two strings S1 and S2 consisting of uppercase English alphabets. Next he wants Sherlock to build a flower in the following way:

He puts both strings perpendicular to each other in such a way that they overlap at the same character. For example, if he has two strings "ABCDEF" and "XXBCZQ", one possible way to make a flower is:

Length of petals in the above flower are 2, 2, 3 and 3.
A flower's ugliness is sum of absolute difference of adjacent petal lengths i.e. i.e. if adjacent petal lengths are L1, L2, L3, L4, then ugliness of flower is |L1 - L2| + |L2 - L3| + |L3 - L4| + |L4 - L1|. 
Sherlock wants to find minimum value of ugliness if we consider all possible flower configurations. Note that a configuration is valid even if any of the petal length is 0.

-----Input-----
First line contains T, number of test cases. Each test case consists of string S1 in one line followed by string S2 in the next line. It is guaranteed that there exists at least one possible way to make a flower.

-----Output-----
For each test case, output in one line the required answer.

-----Constraints-----
- 1 ≤ T ≤ 10
- 1 ≤ length(S1), length(S2) ≤ 105

-----Example-----
Input:
2
ABCDE
XXBCZQ
BBB
BBBBBB

Output: 
2
6

-----Explanation-----

Test case 1:

If we keep the configuration shown in statement, the ugliness is 2, which is minimum possible.

Test case 2:

One of the best configurations is

B 
B B B  B  B B
B

where petal lengths are 1, 3, 1, 2.
user: Vision has finally made it to Wakanda to get his MindStone extracted. The MindStone was linked to his brain in a highly sophisticated manner and Shuri had to solve a complex problem to extract the stone. The MindStone had $n$ integers inscribed in it and Shuri needs to apply the prefix sum operation on the array $k$ times to extract the stone.
Formally, given $n$ integers $A[1], A[2] ..... A[n]$ and a number $k$, apply the operation
$A[i] = \sum_{j=1}^{i} A[j]$
on the array $k$ times.
Finally Shuri needs to apply $modulo$ $(10^9 + 7)$ operation to each element of the array. Can you help Shuri accomplish this task before Thanos gets to them?

-----Input:-----
- First line of the input consists of two space separated integers $n$ and $k$. 
- Second line contains $n$ space separated integers $A[1] .. A[n]$.

-----Output:-----
In a single line print $n$ space separated integers, the values of the resultant array after applying all the operations.

-----Constraints-----
- $1 \leq n \leq 1000$
- $1 \leq k \leq 10^{12}$
- $1 \leq A[i] \leq 10^9$

-----Subtasks-----
- 20 Points: $1 \leq k \leq 1000$
- 30 Points: $1 \leq k \leq 1000000$
- 50 Points: Original Constraints

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

-----Sample Output:-----
$3$ $10$ $18$ $31$

-----EXPLANATION:-----
After applying the prefix sum operation once the array becomes -> $3$ $7$ $8$ $13$
After applying the prefix sum operation for the second time, the array becomes -> $3$ $10$ $18$ $31$
After applying $modulo$ $(10^9 +7)$ operation, array becomes -> $3$ $10$ $18$ $31$
user: You are given a sequence of integers $A_1, A_2, \dots, A_N$.
You should choose an arbitrary (possibly empty) subsequence of $A$ and multiply each element of this subsequence by $-1$. The resulting sequence should satisfy the following condition: the sum of elements of any contiguous subsequence with length greater than 1 is strictly positive.
You should minimise the sum of elements of the resulting sequence. Find one such sequence with the minimum possible sum.

-----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 a single integer $N$.
- 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 $N$ space-separated integers $B_1, B_2, \dots, B_N$. For each valid $i$, $B_i$ must be equal to either $A_i$ (the sign of this element did not change) or $-A_i$ (the sign of this element changed).
If there is more than one answer, you may output any one.

-----Constraints-----
- $1 \le T \le 10^5$
- $2 \le N \le 10^5$
- $1 \le A_i \le 10^9$ for each valid $i$
- the sum of $N$ for all test cases does not exceed $5 \cdot 10^5$

-----Subtasks-----
Subtask #1 (20 points):
- $1 \le T \le 200$
- $2 \le N \le 10$
Subtask #2 (30 points):
- $1 \le T \le 1,000$
- $N \le 2,000$
Subtask #3 (50 points): original constraints

-----Example Input-----
4
4
4 3 1 2
6
1 2 2 1 3 1
5
10 1 2 10 5
4
1 2 1 2

-----Example Output-----
4 3 -1 2
-1 2 2 -1 3 -1
10 -1 2 10 -5
1 2 -1 2

-----Explanation-----
Example case 1: If we change only the sign of $A_3$, we get a sequence $\{4, 3, -1, 2\}$ with sum $8$. This sequence is valid because the sums of all its contiguous subsequences with length $> 1$ are positive. (For example, the sum of elements of the contiguous subsequence $\{A_3, A_4\}$ equals $-1 + 2 = 1 > 0$.)
There are only two valid sequences $\{4, 3, -1, 2\}$ and $\{4, 3, 1, 2\}$ with sums $8$ and $10$ respectively, so this sequence has the smallest possible sum.
For instance, the sequence $\{4, -3, 1, 2\}$ isn't valid, because the sum of $\{A_2, A_3, A_4\}$ equals $-3 + 1 + 2 = 0 \le 0$.
user: A squarer is a simple and convenient device. You give it some positive integer X and it calculates its square.
Leha is implementing a module of this device which is responsible for squaring the numbers consisting of multiple repetitions of one digit. But it turned out that it's not as simple as he thought.
Please help him now!

-----Input-----
The first line contains one integer T denoting the number of testcases. The descriptions of T test cases follow.
Each of the following T lines contain 2 space-separated integers - N and D, respectively. It means that the number X in the corresponding testcase consists of the digit D repeated N times (in decimal representation).

-----Output-----
As the answer can be very large, we ask you to output its hash which is computed in the following way:
Let's consider the integer answer Y as a 0-indexed array starting from its leftmost digit. The hash function is calculated as:
p0*Y[0] + p1*Y[1] + ... + pM-1*Y[M-1] modulo 109 + 7 
where M is the length of the array representation of Y and p equals 23.

-----Constraints-----
- 1 ≤ T ≤ 20
- 1 ≤ D ≤ 9
- Subtask 1 (16 points): 1 ≤ N ≤ 9
- Subtask 2 (25 points): 1 ≤ N ≤ 100
- Subtask 3 (27 points): 1 ≤ N ≤ 2 × 104
- Subtask 4 (32 points): 1 ≤ N ≤ 106

-----Example-----
Input:3
1 4
3 6
3 5

Output:139
40079781
32745632

-----Explanation-----
In the first test case, X = 4 and Y = 16. Its hash equals 1*1 + 23*6 = 139.
user: Chef has $N$ points (numbered $1$ through $N$) in a 2D Cartesian coordinate system. For each valid $i$, the $i$-th point is $(x_i, y_i)$. He also has a fixed integer $c$ and he may perform operations of the following type: choose a point $(x_i, y_i)$ and move it to $(x_i + c, y_i + c)$ or $(x_i - c, y_i - c)$.
Now, Chef wants to set up one or more checkpoints (points in the same coordinate system) and perform zero or more operations in such a way that after they are performed, each of his (moved) $N$ points is located at one of the checkpoints.
Chef's primary objective is to minimise the number of checkpoints. Among all options with this minimum number of checkpoints, he wants to choose one which minimises the number of operations he needs to perform.
Can you help Chef find the minimum number of required checkpoints and the minimum number of operations he needs to perform to move all $N$ points to these checkpoints?

-----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 $c$.
- $N$ lines follow. For each valid $i$, the $i$-th of these lines contains two space-separated integers $x_i$ and $y_i$.

-----Output-----
For each test case, print a single line containing two integers ― the minimum number of checkpoints and the minimum number of moves.

-----Constraints-----
- $1 \le T \le 5$
- $1 \le N \le 5 \cdot 10^5$
- $|x_i|, |y_i| \le 10^9$ for each valid $i$
- $0 < c \le 10^9$
- the sum of $N$ over all test cases does not exceed $5 \cdot 10^5$

-----Example Input-----
1
3 1
1 1
1 0
3 2

-----Example Output-----
2 2

-----Explanation-----
Example case 1: One optimal solution is to set up checkpoints at coordinates $(1, 1)$ and $(1, 0)$. Since the points $(1, 1)$ and $(1, 0)$ are already located at checkpoints, Chef can just move the point $(3, 2)$ to the checkpoint $(1, 0)$ in two moves: $(3, 2) \rightarrow (2, 1) \rightarrow (1, 0)$.
user: There exist certain strings, known as $Unique$ $Strings$. They possess a unique property: 
- The character 'c' gets converted to "ff" and the character 'k' gets converted to "gg". Any letter besides 'c' and 'k' does not get converted to any other character.
Your job is to count the number of strings that could possibly be represented by a given unique string. Since the value could be very large, output the remainder when divided by $10^9+7$.
Note that if the given string is not a unique string, i.e. it contains either 'c' or 'k', output $0$.

-----Input:-----
- The first line of input contains a string, $s$.

-----Output:-----
- Output in a single line the possible number of strings modulo $10^9+7$.

-----Constraints-----
- $1 \leq |s| \leq 10^5$
where |s| denotes length of string.

-----Sample Input 1:-----
thing

-----Sample Input 2:-----
ggdffn

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

-----Sample Input 4:-----
cat

-----Sample Output 1:-----
1

-----Sample Output 2:-----
4

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

-----Sample Output 4:-----
0

-----EXPLANATION:-----
The possible strings that can be represented by the given string in each of the examples are as follows:
$1)$ 'thing'
$2)$ 'ggdffn','kdffn','ggdcn','kdcn'
$3)$ 'fff','cf','fc'
$4)$ Since the string 'cat' contains 'c', it is certain that this string is not a unique string. Hence, the output is $0$.
user: Master Shifu is training Po to become The Dragon Warrior and as a final assignment he must obtain maximum deliciousness from dumplings. There are  $N$ plates of dumplings in front of him with deliciousness $A_1, A_2, \ldots, A_N$, Po can choose any number of continuous plates of  dumplings. The total deliciousness is the sum of deliciousness of all the  chosen dumplings.
What is the minimum number of plates he must choose so that total deliciousness is maximum possible?
Note: Po must choose atleast one plate.

-----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 a single integer $N$.
- 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.

-----Constraints-----
- $1 \le T \le 10$
- $1 \le N \le 2 \cdot 10^5$
- $0 \le A_i \le 10^9$

-----Sample Input:-----
2
4
1 2 3 4
5
3 2 0 3 0

-----Sample Output:-----
4
4
user: Sebi lives in Chefland where the government is extremely corrupt that usually makes fool out of public by announcing eye catching but non-sustainable schemes. Recently there was a move to increase tourism in the country that was highly lauded. Sebi wants to examine whether the move has some potential or is a hogwash as usual.
The Chefland is a city with very old road infrastructure. The city has N tourist places. All the places are reachable from each other. The corrupt administrators of the city constructed as few roads as possible just ensuring that all the places are reachable from each other, and those too have now gone old with potholes every here and there. Upon this, there is a toll tax for each road too, which you have to pay once for using that road. Once you pay the tax for a road, you can visit it again as many times as possible.
The tourists coming to Chefland usually want to see all the N nice places. They usually have visit in their own vehicle and stay for few days. Also, they are usually not very rich, they want to pay as less toll tax as possible. For promoting tourism, the government offered their citizens a scheme. It was announced that citizens can choose any two places and the government will build a high class road between those two places and that too without any toll tax. Note that citizens may choose to have a high class road between two cities which already have an old road between them.
Sebi is very sceptical of the claims of the announcement. So, he wants to understand the expected toll tax a tourist has to pay to tour the entire city considering that the citizens of Chefland vote for the two cities for constructing high road uniformly randomly. Can you please him in finding this?

-----Input-----
There is a single test case per test file.
The first line of the input contains an integer N denoting the number of tourist spots in Chefland.
Each of the he next N - 1 lines contains three space separated integers u, v, c, denoting that there is a road between tourist spot u and v which has a toll tax of c Rs.

-----Output-----
Output a single line containing the expected toll tax a tourist has to pay for visiting all the N spots after the construction of new road. Your answer will be considered correct if it has an absolute error less than or equal to 1e-2.

-----Constraints-----
- 2 ≤ N ≤ 105
- 1 ≤ u, v ≤ N
- 0 ≤ c ≤ 106

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

Output:
2.333333

-----Explanation-----
Assume that the citizens construct the high class road between city 1 and 2. A tourist can visit all the places by just paying a toll tax of 2 Rs.
If the high class road is constructed between city 1 and 3. All the places then can be visited by just paying a toll tax of 3 Rs.
If the cities 2 and 3 are connected by the high class road. All the places can be visited by paying a toll tax of 2Rs. 
Hence expected Rs. that a tourist has to pay in toll tax will be (2 + 3 + 2) / 3 = 7 / 3 = 2.333333
user: The students of Codechef Middle School are visiting an amusement park. The children want to go on a ride, however, there is a minimum height requirement of $X$ cm. Determine if the children are eligible to go on the ride. 
Print "Yes" if they are eligible, "No" otherwise.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains of a single line of input, two integers $H$ which is a child's height in cm and $X$ which is the minimum permissible height. 

-----Output:-----
For each testcase, output in a single line $"Yes"$ or $"No"$. You cannot give your answer as "YeS", "YES", "yes" or any other variation.

-----Constraints-----
- $1 \leq T \leq 10^4$
- $50 \leq H \leq 200$
- $50 \leq X \leq 200$

-----Sample Input:-----
2
120 100
90 100

-----Sample Output:-----
Yes
No

-----EXPLANATION:-----
The first child has height more than minimum permissible height, so he can go on the ride while the other person cannot!
user: Chef Vivek is good in mathematics and likes solving problems on prime numbers. One day his friend Jatin told him about Victory numbers. Victory number can be defined as a number formed after summing up all the prime numbers till given number n. Now, chef Vivek who is very fond of solving questions on prime numbers got busy in some other tasks. Your task is to help him finding victory number.

-----Input:-----
- First line will contain $T$, number of test cases. Then the test cases follow. 
- Each test case contains of a single line of input $N$ till which sum of all prime numbers between 1 to n has to be calculated.

-----Output:-----
For each test case, output in a single line answer to the victory number.

-----Constraints-----
- $1 <= T <= 1000$
- $1 <= N <= 10^6$

-----Sample Input:-----
3
22
13
10

-----Sample Output:-----
77
41
17
user: You were strolling outside the restaurant at the end of the universe. On a metaspiral path you stumble upon a weird device which takes a three-digit number as input and processes it. The Hitchhiker's guide to the galaxy explains that it processes the input in the following manner: 
- Multiplies it with 13, followed by 11 and then 7          
- Outputs all the distinct three-digit numbers possible from the digits of the new number (each digit can only be used once)          
Your friend Zaphod is in a playful mood, and does the following with the device-           
- Given a three-digit positive number $K$, he feeds it to the device for processing.          
- He then takes the numbers it gives as output, and send each of them through the device and again collect all the numbers sent out.          
- Repeats the above step $N$ times.          
To test your wit, he challenges you to find the number of distinct 3-digit numbers which the device outputs over the $N$ steps. Can you?

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

-----Output:-----
For each testcase, output a single integer denoting the number of distinct 3-digit numbers which the device outputs over the $N$ steps.

-----Constraints-----
- $1 \leq T \leq 1000$ 
- $5 \leq N \leq 10^9$ 
- Each digit of $K$ is non-zero           

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

123 5         

-----Sample Output:-----
27
user: Gru has not been in the limelight for a long time and is, therefore, planning something particularly nefarious. Frustrated by his minions' incapability which has kept him away from the limelight, he has built a transmogrifier — a machine which mutates minions.

Each minion has an intrinsic characteristic value (similar to our DNA), which is an integer. The transmogrifier adds an integer K to each of the minions' characteristic value. 

Gru knows that if the new characteristic value of a minion is divisible by 7, then it will have Wolverine-like mutations.

Given the initial characteristic integers of N minions, all of which are then transmogrified, find out how many of them become Wolverine-like.

-----Input Format:-----
The first line contains one integer, T, which is the number of test cases. Each test case is then described in two lines.
The first line contains two integers N and K, as described in the statement.
The next line contains N integers, which denote the initial characteristic values for the minions.

-----Output Format:-----
For each testcase, output one integer in a new line, which is the number of Wolverine-like minions after the transmogrification.

-----Constraints:-----
- 1 ≤ T ≤ 100
- 1 ≤ N ≤ 100
- 1 ≤ K ≤ 100
- All initial characteristic values lie between 1 and 105, both inclusive.

-----Example-----
Input:
1
5 10
2 4 1 35 1

Output:
1

-----Explanation:-----
After transmogrification, the characteristic values become {12,14,11,45,11}, out of which only 14 is divisible by 7. So only the second minion becomes Wolverine-like.
user: The Jones Trucking Company tracks the location of each of its trucks on a grid similar to an (x, y) plane. The home office is at the location (0, 0). Read the coordinates of truck A and the coordinates of truck B and determine which is closer to the office.

-----Input:-----
The first line of the data set for this problem is an integer representing the number of collections of data that follow. Each collection contains 4 integers: the x-coordinate and then the 
y-coordinate of truck A followed by the x-coordinate and then the  y-coordinate of truck B.

-----Output:-----
All letters are upper case.
The output is to be formatted exactly like that for the sample output given below.

-----Assumptions:-----
The x-coordinate is in the range –20 .. 20. The y-coordinate is in the range –20 .. 20.

-----Discussion:-----
The distance between point #1 with coordinates (x1, y1) and point #2 with coordinates (x2, y2) is:

-----Sample Input:-----
4
3 -2 -5 -3
0 6 1 2
-7 8 4 -1
3 3 -2 2

-----Sample Output:-----
A IS CLOSER
B IS CLOSER
B IS CLOSER
B IS CLOSER
user: Chef made $N$ pieces of cakes, numbered them $1$ through $N$ and arranged them in a row in this order. There are $K$ possible types of flavours (numbered $1$ through $K$); for each valid $i$, the $i$-th piece of cake has a flavour $A_i$.
Chef wants to select a contiguous subsegment of the pieces of cake such that there is at least one flavour which does not occur in that subsegment. Find the maximum possible length of such a subsegment of cakes.

-----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 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 maximum length of a valid subsegment.

-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N \le 10^5$
- $2 \le K \le 10^5$
- $1 \le A_i \le K$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $10^6$

-----Subtasks-----
Subtask #1 (50 points):
- $N \le 10^3$
- $K = 2$
- the sum of $N$ over all test cases does not exceed $10^4$
Subtask #2 (50 points): original constraints

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

-----Example Output-----
3
5