meetforever/GRPO_CL huggingface dataset:
user: You are given a weighted graph with $N$ nodes and $M$ edges. Some of the nodes are marked as special nodes. Your task is to find the shortest pairwise distance between any two different special nodes.

-----Input-----
- The first line of the input contains three space-separated integers $N$, $M$ and $K$ denoting the number of nodes, the number of edges, and the number of special nodes. 
- The next line contains $K$ space-separated distinct integers $A_{1}$, $A_{2}$, $\ldots$, $A_{K}$, denoting the special nodes.
- The next $M$ lines each contain three space-separated integers - $X$, $Y$, $Z$, denoting an edge connecting the nodes $X$ and $Y$, with weight $Z$.

-----Output-----
Output the shortest pairwise distance between any two different special nodes.

-----Constraints-----
- The given graph is connected.
- The given graph doesn't contain self loops and multiple edges.
- $1 \leq A_{i} \leq N$
- $1 \leq Z_{j} \leq 10^{4}$
- $1 \leq X_{j}, Y_{j} \leq N$

-----Subtasks-----
Subtask #1 (20 points): 
- $2 \leq N \leq 300$
- $N-1 \leq M \leq \frac{N \cdot (N-1)}{2}$
- $2 \leq K \leq N$
Subtask #2 (25 points):
- $2 \leq N \leq 10^5$
- $N-1 \leq M \leq 10^5$
- $2 \leq K \leq 10$
Subtask #3 (55 points):
- $2 \leq N \leq 10^5$
- $N-1 \leq M \leq 3 \cdot 10^5$
- $2 \leq K \leq 10^4$

-----Example Input-----
5 5 3
1 3 5
1 2 3
2 3 4
3 4 1
4 5 8
1 5 19

-----Example Output-----
7

-----Explanation-----
Nodes $1$, $3$, and $5$ are special nodes. Shortest distance between nodes $1$ and $3$ is $7$, and that between nodes $3$ and $5$ is $9$. Shortest distance between nodes $1$ and $5$ is $16$. Minimum of these distances is $7$. Hence answer is $7$.
user: Sereja has two integers — A and B — in 7-ary system. He wants to calculate the number C, such that B * C = A. It is guaranteed that B is a divisor of A.

Please, help Sereja calculate the number C modulo 7L.

-----Input-----

First line of input contains an integer T — the number of test cases. T tests follow.

For each test case, the first line contains the integer A, and the second line contains the integer B, and the third line contains the integer L. A and B are given in 7-ary system.

-----Output-----
Output the answer in 7-ary system.

-----Constraints-----
- 1 ≤ T ≤ 10
- A and B are both positive integers.
- Length of A is a positive integer and doesn't exceed 106.
- L and length of B are positive integers and do not exceed 10000.

-----Subtasks-----
- Sub task #1 (20 points): Length of A is a positive integer and doesn't exceed 20.
- Sub task #2 (30 points): Length of A is a positive integer and doesn't exceed 2000.
- Sub task #3 (50 points): Original constraints.

-----Example-----
Input:3
21
5
10
202
13
1
202
13
2

Output:3
3
13
user: There are $N$ villages numbered $1$ to $N$. The villages are connected through bi-directional paths in between them. The whole network is in the form of a tree. 
Each village has only $1$ fighter but they help each other in times of crisis by sending their fighter to the village in danger through paths along the villages. Defeating a fighter will mean conquering his village. In particular, If village $X$ is under attack, all villages having a path to $X$ will send their fighters for help. 
Naruto wants to conquer all the villages. But he cannot take on so many fighters at the same time so he plans to use  a secret technique with which he can destroy  any $1$ village (along with paths connected to it) in the blink of an eye.  However, it can be used only once. He realized that if he destroys any village, say $X$, the maximum number of fighters he has to fight at once reduces to $W$. He wants $W$ to be as small as possible. Help him find the optimal $X$.
In case of multiple answers, choose the smallest value of $X$.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- First Line contains $N$.
- Next $N - 1$ lines contain $U, V$, denoting a path between village $U$ and $V$. 

-----Output:-----
- For each Test case, print in a new line, optimal $X$ and corresponding value of $W$.

-----Constraints-----
- $1 \leq T \leq 10$
- $3 \leq N \leq 10^5$
- $1 \leq U, V \leq N$ 
- $U != V$ 

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

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

-----EXPLANATION:-----
Sample 1:  By destroying village $1$,  The fighters Naruto will be fighting at the same time will be from villages $[2, 4]$ and $[3, 5]$.  For this $W$ = $2$. No other choice can give lesser $W$. Hence $1$ is optimal choice.
user: Istiak is learning about arithmetic progressions. Today, he wrote an arithmetic sequence on a piece of paper. Istiak was very happy that he managed to write an arithmetic sequence and went out for lunch.
Istiak's friend Rafsan likes to irritate him by playing silly pranks on him. This time, he could have chosen one element of Istiak's sequence and changed it. When Istiak came back, he was devastated to see his sequence ruined — it became a sequence $a_1, a_2, \ldots, a_N$ (possibly identical to the original sequence, if Rafsan did not change anything, in which case Istiak is just overreacting). Help him recover the original sequence.
Formally, you have to find an arithmetic sequence $b_1, b_2, \ldots, b_N$ which differs from $a$ in at most one position. $b$ is said to be an arithmetic sequence if there is a real number $d$ such that $b_i - b_{i-1} = d$ for each $i$ ($2 \le i \le N$). If there are multiple valid solutions, you may find any one.

-----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 $N$ space-separated integers $b_1, b_2, \ldots, b_N$. It is guaranteed that a valid solution exists.

-----Constraints-----
- $4 \le N \le 10^5$
- $|a_i| \le 10^9$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $5 \cdot 10^5$

-----Example Input-----
3
4
1 3 10 7
5
-10 -5 0 5 10
4
2 2 2 10

-----Example Output-----
1 3 5 7
-10 -5 0 5 10
2 2 2 2

-----Explanation-----
Example case 1: Rafsan changed the third element from $5$ to $10$.
Example case 2: No elements were changed.
Example case 3: Rafsan changed the fourth element from $2$ to $10$.
user: Prime numbers are arranged in a ordered list U$U$, in increasing order. Let S$S$ be a sublist of U$U$ with a unique property that for every element A$A$ belonging to list S$S$, if i$i$ denotes the index of A$A$ in list U$U$, than i$i$ also belongs to list U$U$.
Given N$N$, find sum of first N$N$ elements of list S$S$, assuming 1-based indexing.
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 has an integer N$N$ .

-----Output:-----
For each test case, print a single integer denoting the sum of first N$N$ elements of set S$S$ modulo 109+7$10^{9}+7$.

-----Constraints-----
- 1≤T≤10000$1 \leq T \leq 10000$
- 1≤N≤1000$1 \leq N \leq 1000$

-----Subtasks-----
- 
20 points : 
- 
1≤T≤10000$1 \leq T \leq 10000$
- 
1≤N≤10$1 \leq N \leq 10$
- 
20 points :
- 
1≤T≤100$1 \leq T \leq 100$
- 
1≤N≤100$1 \leq N \leq 100$
- 
60 points : Original Constraints

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

1
2

-----Sample Output:-----
3
8

-----EXPLANATION:-----
Example case 1: 
First few elements of set S$S$ are  {3,5,11…}  , so sum is 3.
Example case 2: 
Sum is 3+5=8.
user: Two integers A and B are the inputs. Write a program to find GCD and LCM of A and B.

-----Input-----

The first line contains an integer T, total number of testcases. Then follow T lines, each line contains an integer A and B. 

-----Output-----
Display the GCD and LCM of A and B separated by space respectively. The answer for each test case must be displayed in a new line.

-----Constraints-----
- 1 ≤ T ≤ 1000
- 1 ≤ A,B ≤ 1000000

-----Example-----
Input
3 
120 140
10213 312
10 30

Output

20 840
1 3186456
10 30
user: Soma is a fashionable girl. She absolutely loves shiny stones that she can put on as jewellery accessories. She has been collecting stones since her childhood - now she has become really good with identifying which ones are fake and which ones are not.  Her King requested for her help in mining precious stones, so she has told him which all stones are jewels and which are not. Given her description, your task is  to count the number of jewel stones. 

More formally, you're given a string J composed of latin characters where each character is a jewel. You're also given a string S composed of latin characters where each character is a mined stone. You have to find out how many characters of S are in J as well. 

-----Input-----

First line contains an integer T denoting the number of test cases. Then follow T test cases. Each test case consists of two lines, each of which contains a string composed of English lower case and upper characters. First of these is the jewel string J and the second one is stone string S. 
You can assume that  1 <= T <= 100, 1 <= |J|, |S| <= 100


-----Output-----
Output for each test case, a single integer, the number of jewels mined. 

-----Example-----
Input:
4
abc
abcdef
aA
abAZ
aaa
a
what
none

Output:
3
2
1
0
user: There are total N friends went to Chef's Pizza shop. There they bought a pizza. Chef divided the pizza into K equal slices. Now you have to check whether these K pizza slices can be distributed equally among the friends. Also given that every person should get at least one slice. If the above conditions are possible then print "YES" otherwise print "NO".

-----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 integers N.
The second line of each test case contains K.

-----Output:-----
For each test case, print a single line containing "YES" if the given conditions are true else "NO" if the given conditions are false.

-----Constraints-----
1<=T<=10
1<=N<=10^6
1<=K<=10^6

-----Sample Input:-----
2
10
20
12
5

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

-----EXPLANATION:-----
Explanation case 1: since there are 10 friends and 20 pizza slice, so each can get 2 slices, so "YES".
Explanation case 2: Since there are 12 friends and only 5 pizza slice, so there is no way pizza slices can be distributed equally and each friend gets at least one pizza slice, so "NO".
user: Every character in the string “IITMANDI” is given a certain number of points. You are given a scrabble board with only one row. The input contains the positions of score modifiers such as: Double Letter, Triple Letter, Double Word and Triple Word. You need to find the best position to place the string “IITMANDI” such that your score is maximized. 
Double Letter - Doubles the number of points you get for the letter placed on the double letter.
Triple Letter - Triples the number of points you get for the letter placed on the triple letter.
Double Word - Doubles the number of points you get for the word. Applied after applying above modifiers.
Triple Word - Triples the number of points you get for the word. Applied after applying the above modifiers.
The word has to be read from left to right. You can’t place it in the reverse direction.

The letters have to be placed continuously on the board.

If there is no modifier or a double word or triple word modifier before a tile, it's score is added to the total score. The double word and triple modifiers are applied at the end.

-----Input Format-----
- First line containes a single integer $T$ - the number of test cases.
- First line of each test case contains a single integer $N$ - the size of the board.    
- Second line of each test case contains a string of size $N$ representing the board according to the following convention:

'.' - No modifier

'd' - Double letter

't' - Triple letter

'D' - Double word

'T' - Triple word     
- Third line of each test case contains 8 integers corresponding to the points associated with each letter of the string "IITMANDI". Note that the 3 'I's in IITMANDI cannot be interchanged freely. The score of the first 'I' will be equal to the first integer, score of the second 'I' will be equal to the second integer and the score of the last 'I' will be equal to the last integer.

-----Output Format-----
For each test case, output a single integer in a new line, the maximum possible score. 

-----Constraints-----
$ 1 \leq T \leq 1000 $
$ 8 \leq N \leq 100 $
$ 0 \leq $ Points for each character $ \leq 10^5 $ 

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

10

..d.t.D..d

10 11 12 9 8 10 11 15

22

dtDtTD..ddT.TtTdDT..TD

12297 5077 28888 17998 12125 27400 31219 21536

-----Sample Output-----
270

35629632
user: Let X be the set of all integers between 0 and n-1. Suppose we have a collection S1, S2, ..., Sm of subsets of X. Say an atom A is a subset of X such that for each Si we have either A is a subset of Si or A and Si do not have any common elements.

Your task is to find a collection A1, ..., Ak of atoms such that every item in X is in some Ai and no two Ai, Aj with i ≠ j share a common item. Surely such a collection exists as we could create a single set {x} for each x in X. A more interesting question is to minimize k, the number of atoms.

-----Input-----

The first line contains a single positive integer t ≤ 30 indicating the number of test cases. Each test case begins with two integers n,m where n is the size of X and m is the number of sets Si. Then m lines follow where the i'th such line begins with an integer vi between 1 and n (inclusive) indicating the size of Si. Following this are vi distinct integers between 0 and n-1 that describe the contents of Si.

You are guaranteed that 1 ≤ n ≤ 100 and 1 ≤ m ≤ 
30. Furthermore, each number between 0 and n-1 will appear in at least one set Si.

-----Output-----

For each test case you are to output a single integer indicating the minimum number of atoms that X can be partitioned into to satisfy the constraints.

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

Output:
3
4
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:-----
5
1
2
3
4
5

-----Sample Output:-----
*
*
**
*
**
***
*
**
* *
****
*
**
* *
*  *
*****

-----EXPLANATION:-----
No need, else pattern can be decode easily.
user: The Quark Codejam's number QC(n, m) represents the number of ways to partition a set of n things into m nonempty subsets. For example, there are seven ways to split a four-element set into two parts:

{1, 2, 3} ∪ {4}, {1, 2, 4} ∪ {3}, {1, 3, 4} ∪ {2}, {2, 3, 4} ∪ {1},

{1, 2} ∪ {3, 4}, {1, 3} ∪ {2, 4}, {1, 4} ∪ {2, 3}.

We can compute QC(n, m) using the recurrence,

QC(n, m) = mQC(n − 1, m) + QC(n − 1, m − 1), for integers 1 < m < n.

but your task is a somewhat different: given integers n and m, compute the parity of QC(n, m), i.e. QC(n, m) mod 2.

Example : 

QC(4, 2) mod 2 = 1. 
Write a program that reads two positive integers n and m, computes QC(n, m) mod 2, and writes the

result.

-----Input-----
The input begins with a single positive integer on a line by itself indicating the number of the cases. This line is followed by the input cases.

The input consists two integers n and m separated by a space, with 1 ≤ m ≤ n ≤ 1000000000.

-----Output-----
For each test case, print the output.

The output should be the integer S(n, m) mod 2.
Sample Input
1

4 2
Sample Output
1
user: Chef loves triangles. But the chef is poor at maths. Given three random lengths Chef wants to find if the three sides form a right-angled triangle or not. Can you help Chef in this endeavour?

-----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, three Integers $A,B and C$

-----Output:-----
For each test case, output in a single line "YES" if it is possible to form a triangle using the given numbers or "NO" if it is not possible to form a triangle.

-----Constraints-----
- $1 \leq T \leq 1000000$
- $0 \leq A,B,C \leq 100$

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

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

-----EXPLANATION:-----
3,4,5 forms a right-angled triangle. 1, 3 and 4 does not form a right-angled triangle.
user: Increasing COVID cases have created panic amongst the people of Chefland, so the government is starting to push for production of a vaccine. It has to report to the media about the exact date when vaccines will be available.
There are two companies which are producing vaccines for COVID. Company A starts producing vaccines on day $D_1$ and it can produce $V_1$ vaccines per day. Company B starts producing vaccines on day $D_2$ and it can produce $V_2$ vaccines per day. Currently, we are on day $1$.
We need a total of $P$ vaccines. How many days are required to produce enough vaccines? Formally, find the smallest integer $d$ such that we have enough vaccines at the end of the day $d$.

-----Input-----
- The first and only line of the input contains five space-separated integers $D_1$, $V_1$, $D_2$, $V_2$ and $P$.

-----Output-----
Print a single line containing one integer ― the smallest required number of days.

-----Constraints-----
- $1 \le D_1, V_1, D_2, V_2 \le 100$
- $1 \le P \le 1,000$

-----Subtasks-----
Subtask #1 (30 points): $D_1 = D_2$
Subtask #2 (70 points): original constraints

-----Example Input 1-----
1 2 1 3 14

-----Example Output 1-----
3

-----Explanation-----
Since $D_1 = D_2 = 1$, we can produce $V_1 + V_2 = 5$ vaccines per day. In $3$ days, we produce $15$ vaccines, which satisfies our requirement of $14$ vaccines.

-----Example Input 2-----
5 4 2 10 100

-----Example Output 2-----
9

-----Explanation-----
There are $0$ vaccines produced on the first day, $10$ vaccines produced on each of days $2$, $3$ and $4$, and $14$ vaccines produced on the fifth and each subsequent day. In $9$ days, it makes a total of $0 + 10 \cdot 3 + 14 \cdot 5 = 100$ vaccines.
user: “Jesse, you asked me if I was in the meth business, or the money business… Neither. I’m in the empire business.”
Walter’s sold his stack in Gray Matter Technologies, a company which he deserved half a credit, for peanuts. Now this company is worth a billion dollar company. Walter wants to get it's shares to have his Empire Business back and he founds an opportunity.  
There are $N$ persons having shares $A_1, A_2, A_3, … A_N$ in this company. Walter can buy these shares with their minimum Sold Values. 
Sold Values of a person's share $ i $ $(1 \leq i \leq N) $ with another person's share $ j $ $ (1 \leq j \leq N) $ is equal to $ A_j+|i-j| $. So, a person's share can have $ N $ possible sold values and Walter has to find minimum sold value among them for each person.
Since Walter has to run his meth business also he asks you to find minimum sold value for each person.

-----Input:-----
- First line will contain $T$, number of test cases. Then the testcases follow. 
- The First line of each test case contains a integer $N$.
- The Second line of each test case contains $N$ space integers namely $A_1,A_2,…A_N$.

-----Output:-----
For each test case, output in single line $N$ space integers denoting minimum sold value for each person.

-----Constraints-----
- $1 \leq T \leq 10^5$
- $1 \leq N \leq 2*10^6 $
- $1 \leq A_i \leq 10^9 $
Sum of $N$ over all test cases will not exceed $2*10^6$.

-----Sample Input:-----
2
5
6 5 5 5 2
5
1 2 3 4 5

-----Sample Output:-----
6 5 4 3 2
1 2 3 4 5

-----Explanation-----
For first case:
- Sold value for index $1$:  $6,6,7,8,6$
- Sold value for index $2$:  $7,5,6,7,5$
- Sold value for index $3$:  $8,6,5,6,4$
- Sold value for index $4$:  $9,7,6,5,3$
- Sold value for index $5$:  $10,8,7,6,2$
Minimum sold value for each index will be $6,5,4,3,2$.
user: The chef is trying to solve some pattern problems, Chef wants your help to code it. Chef has one number K to form new pattern. Help the chef to code this pattern problem.

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

-----Output:-----
For each testcase, output as pattern.

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

-----Sample Input:-----
2
2
4

-----Sample Output:-----
2
12
012
12
2

4
34
234
1234
01234
1234
234
34
4

-----EXPLANATION:-----
No need, else pattern can be decode easily.
user: The Fibonacci sequence is defined as F(n) = F(n-1) + F(n-2). You have developed two sequences of numbers. The first sequence that uses the bitwise XOR operation instead of the addition method is called the Xoronacci number. It is described as follows:
X(n) = X(n-1) XOR X(n-2)
The second sequence that uses the bitwise XNOR operation instead of the addition method is called the XNoronacci number. It is described as follows:
E(n) = E(n-1) XNOR E(n-2)
The first and second numbers of the sequence are as follows:
X(1) = E(1) = a
X(2) = E(2) = b
Your task is to determine the value of max(X(n),E(n)), where n is the n th term of the Xoronacci and XNoronacci sequence.

-----Input:-----
The first line consists of a single integer T denoting the number of test cases.
The first and the only line of each test case consists of three space separated integers a, b and n.

-----Output:-----
For each test case print a single integer max(X(n),E(n)).

-----Constraints-----
- $1 \leq T \leq 1000$
- $2 \leq a,b,n \leq 1000000000000$

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

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

-----EXPLANATION:-----
Xoronacci Sequence : 3 4 7 …….
XNoronacci Sequence : 3 4 0 …….
Here n = 2. Hence max(X(2),E(2)) = 4
user: "I don't have any fancy quotes." - vijju123
Chef was reading some quotes by great people. Now, he is interested in classifying all the fancy quotes he knows. He thinks that all fancy quotes which contain the word "not" are Real Fancy; quotes that do not contain it are regularly fancy.
You are given some quotes. For each quote, you need to tell Chef if it is Real Fancy or just regularly fancy.

-----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 a single string $S$ denoting a quote.

-----Output-----
For each test case, print a single line containing the string "Real Fancy" or "regularly fancy" (without quotes).

-----Constraints-----
- $1 \le T \le 50$
- $1 \le |S| \le 100$
- each character of $S$ is either a lowercase English letter or a space

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

-----Example Input-----
2
i do not have any fancy quotes
when nothing goes right go left

-----Example Output-----
Real Fancy
regularly fancy

-----Explanation-----
Example case 1: "i do not have any fancy quotes"
Example case 2: The word "not" does not appear in the given quote.