meetforever/GRPO_CL huggingface dataset:
user: Anmol gained a lot of weight last semester. So this semester, he decided to run everyday. There is a very long straight road starting at his hostel. There are N poles on the road - P1, P2, P3,..., PN on the road. All the poles lie on the same side of his hostel. The distance between Pi and his hostel is Di.
For 1 ≤ i, j ≤ N, i < j implies Di < Dj
Everyday, Anmol chooses a pole Pi to start running from. He keeps on running until he reaches Pi+K. Whenever he reaches a pole (other than the starting pole), he records the distance traveled since the last pole.

You are given the distances recorded by him today. Your task is to find the number of distinct values of i such that i + K ≤ N and if he starts at Pi and end at Pi+K, he would end up having exactly the same record of distances (in the same order).

-----Input-----
- The first line of the input contains an integer T denoting the number of test cases.
- The first line of each test case contains two space separated integers N and K.
- The next line contains N space separated integers D1, D2,..., DN.
- The next line contains K space separated integers representing the distances recorded by Anmol in the same order.
.

-----Output-----
- For each test case, output a single line containing the answer for that test case.

-----Constraints-----
- 1 ≤ T ≤ 10
- 2 ≤ N ≤ 5 x 104
- 1 ≤ K < N
- 1 ≤ Di ≤ 106

-----Subtasks-----

-----Subtask #1 (20 points)-----
- 1 ≤ N ≤ 1000

-----Subtask #2 (80 points)-----
- Original constraints

-----Example-----
Input:
3
5 1
1 5 10 12 14
5
5 2
5 8 13 16 21
3 5
5 3
2 6 8 11 16
2 3 5

Output:
1
2
1

-----Explanation-----
Example case 1. If he runs from P2 to P3, he will record (5)
Example case 2. He can start at P1 or P3
Example case 3. He can start at P2
user: Chef is a really nice and respectful person, in sharp contrast to his little brother, who is a very nasty and disrespectful person. Chef always sends messages to his friends in all small letters, whereas the little brother sends messages in all capital letters.
You just received a message given by a string s. You don't know whether this message is sent by Chef or his brother. Also, the communication channel through which you received the message is erroneous and hence can flip a letter from uppercase to lowercase or vice versa. However, you know that this channel can make at most K such flips.
Determine whether the message could have been sent only by Chef, only by the little brother, by both or by none.

-----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 denoting the length of the string s and the maximum number of flips that the erroneous channel can make.
- The second line contains a single string s denoting the message you received.

-----Output-----
For each test case, output a single line containing one string — "chef", "brother", "both" or "none".

-----Constraints-----
- 1 ≤ T ≤ 1000
- 1 ≤ N ≤ 100
- 0 ≤ K ≤ N
- s consists only of (lowercase and uppercase) English letters

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

4
5 1
frauD
5 1
FRAUD
4 4
Life
10 4
sTRAWBerry

Output

chef
brother
both
none

-----Explanation-----
Example case 1: Only one flip is possible. So it is possible that Chef sent "fraud" and the channel flipped the last character to get "frauD". However, it is not possible for the brother to have sent "FRAUD", because then it would need 4 flips. Hence the answer is "chef".
Example case 2: Only one flip is possible. So it is possible that the brother sent "FRAUD" and the channel didn't flip anything. However, it is not possible for Chef to have sent "fraud", because then it would need 5 flips. Hence the answer is "brother".
Example case 3: Four flips are allowed. It is possible that Chef sent "life" and the channel flipped the first character to get "Life". It is also possible that the brother sent "LIFE" and the channel flipped the last three characters to get "Life". Hence the answer is "both".
Example case 4: Four flips are allowed. It is not possible that Chef sent "strawberry", because it would need five flips to get "sTRAWBerry". It is also not possible that the brother sent "STRAWBERRY", because that would also need five flips. Hence the answer is "none".
user: Alice likes prime numbers. According to Alice, only those strings are nice whose sum of character values at a prime position is prime. She has a string $S$. Now, she has to count the number of nice strings which come before string $S$( including $S$) in the dictionary and are of the same length as $S$. 
Strings are zero-indexed from left to right.
To find the character value she uses the mapping {'a': 0, 'b':1, 'c':2 ……. 'y': 24, 'z':25} .
For example, for string $abcde$ Characters at prime positions are $'c'$ and $'d'$. c + d = 2 + 3 = 5. Since, 5 is a prime number, the string is $nice$.
Since there could be many nice strings print the answer modulo $10^{9}+7$.

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

-----Output:-----
For each testcase, output in a single line number of nice strings modulo $10^{9}+7$.

-----Constraints-----
- $1 \leq T \leq 10$
- $2 \leq |S| \leq 10^2$
String $S$ contains only lowercase letters.

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

-----Sample Output:-----
10
user: Navnit is a college student and there are $N$ students in his college .Students are numbered from $1$ to $N$.
You are given $M$ facts that "Student $A_i$ and $B_i$".The same fact can be given multiple times .If $A_i$ is a friend of $B_i$ ,then $B_i$ is also a friend of $A_i$ . If $A_i$ is a friend of $B_i$ and $B_i$ is a friend of $C_i$ then $A_i$ is also a friend of $C_i$.
Find number of ways in which two students can be selected in such a way that they are not friends. 

-----Input:-----
- First line will contain two integers $N$ and $M$. 
- Then $M$ lines follow. Each line contains two integers $A_i$ and $B_i$ denoting the students who are friends.

-----Output:-----
For each testcase, output the number of ways in which  two students can be selected in such a way that they are friends.

-----Constraints-----
- $2 \leq N \leq 200000$
- $0 \leq M \leq 200000$
- $1 \leq A_i,B_i \leq N$

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

-----Sample Output:-----
6

-----EXPLANATION:-----
Groups of friend are $[1,2,5]$ and $[3,4]$.Hence the answer is  3 X 2 =6.
user: A number K$K$ is said to be magical if it can be represented as a power of 2 only.That is K$K$=2x$2^{x}$ for some natural number x$x$. 
Given a string of digits S$S$ of length N$N$, Let P be a valid arrangement of S.
By valid arrangement we mean that it should not have any leading zeroes.
Find the sum of all such distinct Pi's, which, when treated as a number is magical.
Two arrangements are said to be distinct, if there is atleast one index where they differ. 
As the sum can be very large, print the sum modulo 109+7$10^{9}+7$.

-----Input:-----
-The first line of the input contains a single integer T$T$ denoting the number of test cases. 
-Only line of each test case contains a string S$S$ of length N$N$, consisting only of digits between 0 to 9.

-----Output:-----
For each test case, print a single integer denoting the sum of all such magical Pi′s$Pi's$ modulo 109+7$10^{9}+7$.
If no such Pi$Pi$ exists print "-1".

-----Constraints-----
- 1≤T≤1000$1 \leq T \leq 1000$
- 2≤N≤1000$2 \leq N \leq 1000$
- String only consists of digits between 0 to 9, both inclusive.

-----Subtasks-----
- 10 points : 1≤N≤5$1 \leq N \leq 5$
- 40 points : 1≤N≤100$1 \leq N \leq 100$
- 50 points : Original Constraints

-----Sample Input:-----
2
35566

31

-----Sample Output:-----
65536

-1

-----EXPLANATION:-----
Only arrangement is 65536.
No arrangement of 31 gives us a power of two.
user: The chef is trying to solve some pattern problems, Chef wants your help to code it. Chef has one number K to form a new pattern. Help the chef to code this pattern problem.

-----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, one integer $K$. 

-----Output:-----
For each test case, output as the pattern.

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq K \leq 100$

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

-----Sample Output:-----
2
24
68
246
81012
141618
2468
10121416
18202224
26283032

-----EXPLANATION:-----
No need, else pattern can be decode easily.
user: You have been recently hired as a developer in CodeChef. Your first mission is to implement a feature that will determine the number of submissions that were judged late in a contest.
There are $N$ submissions, numbered $1$ through $N$. For each valid $i$, the $i$-th submission was submitted at time $S_i$ and judged at time $J_i$ (in minutes). Submitting and judging both take zero time. Please determine how many submissions received their verdicts after a delay of more than $5$ minutes.

-----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 the input contains a single integer $N$.
- $N$ lines follow. For each valid $i$, the $i$-th of these lines contains two space-separated integers $S_i$ and $J_i$.

-----Output-----
For each test case, print a single line containing one integer — the number of submissions for which the judging was delayed by more than 5 minutes.

-----Constraints-----
- $1 \le T \le 100$
- $1 \le N \le 100$
- $1 \le S_i \le J_i \le 300$ for each valid $i$

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

-----Example Input-----
1
5
1 3
4 4
4 10
1 11
2 7

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

-----Explanation-----
Example case 1: The delays of the respective submissions are $2$ minutes, $0$ minutes, $6$ minutes, $10$ minutes and $5$ minutes. Only submissions $3$ and $4$ are delayed by more than $5$ minutes, hence the answer is $2$.
user: Chef recently started working at ABC corporation. Let's number weekdays (Monday through Friday) by integers $1$ through $5$. For each valid $i$, the number of hours Chef spent working at the office on weekday $i$ was $A_i$.
Unfortunately, due to the COVID-19 pandemic, Chef started working from home and his productivity decreased by a considerable amount. As per Chef's analysis, $1$ hour of work done at the office is equivalent to $P$ hours of work done at home.
Now, in order to complete his work properly, Chef has to spend more hours working from home, possibly at the cost of other things like sleep. However, he does not have to do the same work on each day as he would have in the office ― for each weekday, he can start the work for this day on an earlier day and/or complete it on a later day. The only requirement is that his work does not pile up indefinitely, i.e. he can complete his work for each week during the same week. One day has $24$ hours.
If Chef is unable to complete his work for a week during those five weekdays, then he has to work during the weekend too. Chef wishes to know whether he has to work on weekends or if he can complete his work by working only on weekdays. Help him answer that question. (It is possible that Chef would be unable to finish his work even if he worked all the time, but he does not want to know about that.)

-----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 and only line of each test case contains six space-separated integers $A_1$, $A_2$, $A_3$, $A_4$, $A_5$ and $P$.

-----Output-----
For each test case, print a single line containing the string "Yes" if Chef has to work on weekends or "No" otherwise (without quotes).

-----Constraints-----
- $1 \le T \le 1,000$
- $0 \le A_i \le 24$ for each valid $i$
- $1 \le P \le 24$

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

-----Example Input-----
2
14 10 12 6 18 2
10 10 10 10 10 3

-----Example Output-----
No
Yes

-----Explanation-----
Example case 1: Here, $P=2$, so the number of hours Chef has to work from home to handle his workload for days $1$ through $5$ is $[28,20,24,12,36]$. If he works for full $24$ hours on each of the five weekdays, he finishes all the work, so he does not have to work on weekends.
Example case 2: No matter what Chef does, he will have to work on weekends.
user: Chef has a garden with $N$ plants arranged in a line in decreasing order of height. Initially the height of the plants are $A_1, A_2, ..., A_N$.
The plants are growing, after each hour the height of the $i$-th plant increases by $i$ millimeters. Find the minimum number of integer hours that Chef must wait to have two plants of the same height.

-----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 $A_1,A_2,..A_N$. 

-----Output:-----
For each test case print a single line containing one integer, the minimum number of integer hours that Chef must wait to have two plants of the same height.

-----Constraints-----
- $1 \leq T \leq 1000$
- $2 \leq N \leq 10^5$
- $0\leq A_i \leq 10^{18}$
- $A_i >A_{i+1}$, for each valid $i$
- The Sum of $N$ over all test cases does not exceed $10^6$

-----Sample Input:-----
1
3
8 4 2

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

-----EXPLANATION:-----
After $2$ hours there are two plants with the same height. 
$[8,4,2] \rightarrow [9,6,5] \rightarrow [10,8,8]$.
user: The snakes want to build a temple for Lord Cobra. There are multiple strips of land that they are looking at, but not all of them are suitable. They need the strip of land to resemble a coiled Cobra. You need to find out which strips do so.
Formally, every strip of land, has a length. Suppose the length of the i-th strip is is Ni, then there will be Ni integers, Hi1, Hi2, .. HiNi, which represent the heights of the ground at various parts of the strip, in sequential order. That is, the strip has been divided into Ni parts and the height of each part is given. This strip is valid, if and only if all these conditions are satisfied:
- There should be an unique 'centre' part. This is where the actual temple will be built. By centre, we mean that there should be an equal number of parts to the left of this part, and to the right of this part.
- Hi1 = 1
- The heights keep increasing by exactly 1, as you move from the leftmost part, to the centre part.
- The heights should keep decreasing by exactly 1, as you move from the centre part to the rightmost part. Note that this means that HiNi should also be 1.
Your job is to look at every strip and find if it's valid or not.

-----Input-----
- The first line contains a single integer, S, which is the number of strips you need to look at. The description of each of the S strips follows
- The first line of the i-th strip's description will contain a single integer: Ni, which is the length and number of parts into which it has been divided.
- The next line contains Ni integers: Hi1, Hi2, .., HiNi. These represent the heights of the various parts in the i-th strip.

-----Output-----
- For each strip, in a new line, output "yes" if is a valid strip, and "no", if it isn't.

-----Constraints-----
- 1 ≤ S ≤ 100 
- 3 ≤ Ni ≤ 100 
- 1 ≤ Hij ≤ 100 

-----Example-----
Input:
7
5
1 2 3 2 1
7
2 3 4 5 4 3 2
5
1 2 3 4 3
5
1 3 5 3 1
7
1 2 3 4 3 2 1
4
1 2 3 2
4
1 2 2 1

Output:
yes
no
no
no
yes
no
no

-----Explanation-----
In the first strip, all the conditions are satisfied, hence it is valid.
In the second strip, it does not start with a 1, and hence is invalid.
In the third strip, it keeps increasing even past the centre, instead of decreasing. Hence invalid.
The fourth strip does not increase and decrease by exactly 1. Hence invalid.
The fifth satisfies all conditions and hence is valid.
The sixth and seventh strip do not have a 'centre' part. Because for every part, there are either more parts to its right than its left, or more parts on its left than its right. Hence both the strips are invalid.
user: Vanja and Miksi have already finished everything for this year at their university, so they decided to spend their free time playing a game with a binary sequence $A_1, A_2, \dots, A_N$ (i.e. a sequence containing only integers $0$ and $1$).
At the beginning of the game, Vanja and Miksi write down the expression $* A_1 * A_2 * A_3 * \ldots * A_N$ (note below that each $*$ is a placeholder and does not denote multiplication).
The players take turns alternately, starting with Vanja. The game lasts $N$ turns. In each turn, the current player must replace the first (leftmost) remaining $*$ by the sign $+$ or $-$ (or, equivalently, by the operation of addition or subtraction).
After the last turn, the boys calculate the resulting value $V$ of the expression. If $|V| \ge K$, the winner is Vanja; otherwise, the winner is Miksi.
Please predict the winner of the game if both players play optimally. 

-----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 — $1$ if Vanja (the first player) is the winner or $2$ if Miksi (the second player) is the winner.

-----Constraints-----
- $1 \le T \le 50$
- $1 \le N \le 3 \cdot 10^4$
- $0 \le K \le 3 \cdot 10^4$
- $0 \le A_i \le 1$ for each valid $i$

-----Example Input-----
2
2 1
1 0
3 5
0 1 0

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

-----Explanation-----
Example case 1: $K = 1$, so if Vanja replaces the first $*$ by $+$, the value of the final expression will be $V = 1$; then, $K \le |V|$, so the winner is Vanja.
Example case 2: $K = 5$, but the absolute value of the final expression cannot be greater than $1$. The winner is Miksi.
user: The chef likes to play with numbers. He takes some integer number x, writes it down on his iPad, and then performs with it n−1 operations of the two kinds:
- divide the number x by 3 (x must be divisible by 3);
- multiply the number x by 2.
After each iteration, Chef writes down the result on his iPad and replaces x with the result. So there will be n numbers on the iPad after all.
You are given a sequence of length n — the numbers that Chef wrote down. This sequence is given in the order of the sequence can mismatch the order of the numbers written on the iPad.
Your problem is to rearrange elements of this sequence in such a way that it can match a possible Chef's game in the order of the numbers written on the board. I.e. each next number will be exactly two times the previous number or exactly one-third of the previous number.
I can give a guarantee that the answer exists.

-----Input:-----
- The first line of the input contains an integer number N i.e the number of the elements in the sequence. 
- The second line of the input contains n integer numbers a1,a2,…, an i.e rearranged (reordered) sequence that Chef can write down on the iPad.

-----Output:-----
Print N integer numbers — rearranged (reordered) input sequence that can be the sequence that Chef could write down on the iPad.
It is guaranteed that the answer exists

-----Constraints-----
- $2 \leq N \leq 100$
- $1 \leq A[i] \leq  3* 10^{18} $

-----Sample Input:-----
6
4 8 6 3 12 9

-----Sample Output:-----
9 3 6 12 4 8 

-----EXPLANATION:-----
In the first example, the given sequence can be rearranged in the following way: [9,3,6,12,4,8]. It can match possible Polycarp's game which started with x=9.
user: There are $N$ cities on a circle, numbered $1$ through $N$. For each $i$ ($1 \le i \le N-1$), cities $i$ and $i+1$ are directly connected by a bidirectional road with length $A_i$, and cities $N$ and $1$ are also directly connected by a bidirectional road with length $A_N$. However, we do not know the lengths of some roads.
For each city $i$, we do know that it has an opposite city — formally, there is a city $j \neq i$ such that the clockwise distance between cities $i$ and $j$ is equal to the counterclockwise distance between these cities.
Please find the lengths of all roads in such a way that the above condition is satisfied and the sum of lengths of all roads is minimised.

-----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 the input contains a single integer $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \dots, A_N$. For each valid $i$, $A_i = -1$ denotes that the length of road $i$ is unknown.

-----Output-----
For each test case, print a line containing the string "NO" if there is no solution or "YES" otherwise. If a solution exists, print a second line containing $N$ space-separated positive integers — the lengths of all roads in your solution. Each of these integers should be $\le 10^9$. If there are multiple solutions, you may print any one.

-----Constraints-----
- $1 \le T \le 100$
- $3 \le N \le 10^5$
- $1 \le A_i \le 10^9$ or $A_i = -1$ for each valid $i$
- the sum of $N$ for all test cases does not exceed $3\cdot 10^5$

-----Subtasks-----
Subtask #1 (10 points): $N \le 4$
Subtask #2 (20 points): $A_i = \pm 1$ for each valid $i$
Subtask #3 (70 points): original constraints

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

-----Example Output-----
YES
1 1 1 1
NO
YES
1 4 1 4
NO
user: The chef is trying to solve some pattern problems, Chef wants your help to code it. Chef has one number K to form a new pattern. Help the chef to code this pattern problem.

-----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, one integer $K$. 

-----Output:-----
For each test case, output as the pattern.

-----Constraints-----
- $1 \leq T \leq 50$
- $1 \leq K \leq 50$

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

-----Sample Output:-----
1
1
23
1
23
456
1
23
4 5
6789
1
23
4 5
6  7
89101112

-----EXPLANATION:-----
No need, else pattern can be decode easily.