meetforever/GRPO_CL huggingface dataset:
user: Chef is the new king of the country Chefland. As first and most important responsibility he wants to reconstruct the road system of Chefland. There are N (1 to N) cities in the country and each city i has a population Pi. Chef wants to build some bi-directional roads connecting different cities such that each city is connected to every other city (by a direct road or through some other intermediate city) and starting from any city one can visit every other city in the country through these roads. Cost of building a road between two cities u and v is Pu x Pv. Cost to build the road system is the sum of cost of every individual road that would be built. 
Help king Chef to find the minimum cost to build the new road system in Chefland such that every city is connected to each other.

-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows. 
First line contains an integer N denoting the number of cities in the country. Second line contains N space separated integers Pi, the population of i-th city.

-----Output-----
For each test case, print a single integer, the minimum cost to build the new road system on separate line.

-----Constraints-----
- 1 ≤ T ≤ 10
- 1 ≤ N ≤ 105
- 1 ≤ Pi ≤ 106

-----Example-----
Input:
2
2
5 10
4
15 10 7 13

Output:
50
266
user: Chef is solving mathematics problems. He is preparing for Engineering Entrance exam. He's stuck in a problem.
$f(n)=1^n*2^{n-1}*3^{n-2} * \ldots * n^{1} $ 
Help Chef to find the value of $f(n)$.Since this number could be very large, compute it modulo $1000000007$.

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

-----Output:-----
For each testcase, output in a single line the value of $f(n)$ mod $1000000007$.

-----Constraints-----
- $1 \leq T \leq 10^6$
- $1 \leq N \leq 10^6$

-----Subtasks-----
Subtask 1(24 points) : 
- $1 \leq T \leq 5000$
- $1 \leq N \leq 5000$
Subtask 2(51 points) : original constraints

-----Sample Input:-----
1
3

-----Sample Output:-----
12
user: It's winter and taking a bath is a delicate matter. Chef has two buckets of water. The first bucket has $v_1$ volume of cold water at temperature $t_1$. The second has $v_2$ volume of hot water at temperature $t_2$. Chef wants to take a bath with at least $v_3$ volume of water which is at exactly $t_3$ temperature. To get the required amount of water, Chef can mix some water obtained from the first and second buckets.
Mixing $v_x$ volume of water at temperature $t_x$ with $v_y$ volume of water at temperature $t_y$ yields $v_x + v_y$ volume of water at temperature calculated as
vxtx+vytyvx+vyvxtx+vytyvx+vy\frac{v_x t_x + v_y t_y}{v_x + v_y}
Help Chef figure out if it is possible for him to take a bath with at least $v_3$ volume of water at temperature $t_3$.
Assume that Chef has no other source of water and that no heat is lost by the water in the buckets with time, so Chef cannot simply wait for the water to cool.

-----Input-----
- The first line contains $n$, the number of test cases. $n$ cases follow.
- Each testcase contains of a single line containing 6 integers $v_1, t_1, v_2, t_2, v_3, t_3$.

-----Output-----
- For each test case, print a single line containing "YES" if Chef can take a bath the way he wants and "NO" otherwise.

-----Constraints-----
- $1 \leq n \leq 10^5$
- $1 \leq v_1, v_2, v_3 \leq 10^6$
- $1 \leq t_1 < t_2 \leq 10^6$
- $1 \leq t_3 \leq 10^6$

-----Sample Input-----
3
5 10 5 20 8 15
5 10 5 20 1 30
5 10 5 20 5 20

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

-----Explanation-----
- Case 1: Mixing all the water in both buckets yields 10 volume of water at temperature 15, which is more than the required 8.
- Case 2: It is not possible to get water at 30 temperature.
- Case 3: Chef can take a bath using only the water in the second bucket.
user: -----Problem Statement-----
One of the things JEC is known for is its GR (Group Recreation) where juniors and seniors do friendly interaction ;P
As for the new session of 2020 seniors decided to have their first GR and give them some treat. Juniors were excited about it they came to college canteen aligned in a line and counted themselves one by one from left to right so that every junior gets his/her treat. But seniors played a game and they will treat only the ones who passes in this game. Game is simple all they need to do is to alternate their language (between Hindi and English) while telling their positions that is if the junior just before you told 2 in English you need to say 3 in Hindi . You do not want to be the one left without a treat. 
You are the junior standing at position $X$ from left and the counting could start from left or right you have to predict which number you have to speak and in which language when your turn comes.

-----Input:-----
- 
First line will contain $T$, number of testcases. Then the testcases follow. 
- 
Each testcase contains 2 lines first consist 2 space separated integers, $N$ (total count) , $X$ (your position from left), next line consist of 2 space separated characters  L or R (Direction from which counting starts L-left, R-Right) and H or E (the language to start counting).

-----Output:-----
For each testcase, output a single line consisting space seperated Integer P and Character L
where P is the number you will speak and L is the language (H or E).

-----Constraints-----
- $1 \leq T \leq 1000$
- $1 \leq N \leq 120$
- $1 \leq X \leq N$

-----Sample Input:-----
2
15 5
L H
20 14
R E

*try to trim extra white spaces like new line during input in case of wrong answer

-----Sample Output:-----
5 H
7 E

-----EXPLANATION:-----
- When counting starts from left with H it alternates like H E H E H….. on the fifth position H comes
- When Count starts from right with E it alternates like E H E H E H E….. with E on the position of 14th student from right.
user: The chef is having one string of English lower case alphabets only. The chef wants to remove all "abc" special pairs where a,b,c are occurring consecutively. After removing the pair, create a new string and again remove "abc" special pair from a newly formed string. Repeate the process until no such pair remains in a string.

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

-----Output:-----
For each testcase, output in a single line answer, new String with no "abc" special pair.

-----Constraints:-----
$T \leq 2 $
$1 \leq String length \leq 1000 $

-----Sample Input:-----
2
aabcc
bababccc

-----Sample Output:-----
ac
bc

-----EXPLANATION:-----
For 1) after removing "abc" at middle we get a new string as ac.
For 2) string = bababccc
newString1 = babcc  // After removing middle "abc"
newString2 = bc   //After removing "abc"
user: "Everything in the universe is balanced. Every disappointment you face in life will be balanced by something good for you! Keep going, never give up."
Let's call a string balanced if all characters that occur in this string occur in it the same number of times.
You are given a string $S$; this string may only contain uppercase English letters. You may perform the following operation any number of times (including zero): choose one letter in $S$ and replace it by another uppercase English letter. Note that even if the replaced letter occurs in $S$ multiple times, only the chosen occurrence of this letter is replaced.
Find the minimum number of operations required to convert the given string to a balanced string.

-----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 $S$.

-----Output-----
For each test case, print a single line containing one integer ― the minimum number of operations.

-----Constraints-----
- $1 \le T \le 10,000$
- $1 \le |S| \le 1,000,000$
- the sum of $|S|$ over all test cases does not exceed $5,000,000$
- $S$ contains only uppercase English letters

-----Subtasks-----
Subtask #1 (20 points):
- $T \le 10$
- $|S| \le 18$
Subtask #2 (80 points): original constraints

-----Example Input-----
2
ABCB
BBC

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

-----Explanation-----
Example case 1: We can change 'C' to 'A'. The resulting string is "ABAB", which is a balanced string, since the number of occurrences of 'A' is equal to the number of occurrences of 'B'.
Example case 2: We can change 'C' to 'B' to make the string "BBB", which is a balanced string.
user: Chef and his competitor Kefa own two restaurants located at a straight road. The position of Chef's restaurant is $X_1$, the position of Kefa's restaurant is $X_2$.
Chef and Kefa found out at the same time that a bottle with a secret recipe is located on the road between their restaurants. The position of the bottle is $X_3$.
The cooks immediately started to run to the bottle. Chef runs with speed $V_1$, Kefa with speed $V_2$.
Your task is to figure out who reaches the bottle first and gets the secret recipe (of course, it is possible that both cooks reach the bottle at the same time).

-----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 five space-separated integers $X_1$, $X_2$, $X_3$, $V_1$ and $V_2$. 

-----Output-----
For each test case, print a single line containing the string "Chef" if Chef reaches the bottle first, "Kefa" if Kefa reaches the bottle first or "Draw" if Chef and Kefa reach the bottle at the same time (without quotes). 

-----Constraints-----
- $1 \le T \le 10^5$
- $|X_1|, |X_2|, |X_3| \le 10^5$
- $X_1 < X_3 < X_2$
- $1 \le V_1 \le 10^5$
- $1 \le V_2 \le 10^5$

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

-----Example Output-----
Kefa
Chef
Draw

-----Explanation-----
Example case 1. Chef and Kefa are on the same distance from the bottle, but Kefa has speed $2$, while Chef has speed $1$.
user: Everybody is worried about Rakesh as the boy does not have much knowledge about the real world. He can not go from one place to another on his own. It's high time he learned to explore the city. He is going to a relative's house situated on the other side of the city on his own. As this is his first time, he is carrying a GPS tracker of a special kind. The tracker continuously sends information to the family of Rakesh about his movement. The information is sent using the following four letters: U, D, R, and L. Those letters indicate the moves taken by Rakesh. 

The city can be considered as a grid. Rakesh starts his journey from (0, 0) position of the grid. His relative's house is situated at (Rx, Ry). Rakesh can move in four directions: up, down, right, or left indicated by U, D, R, and L respectively. 

Any position of the city with x ordinate negative or greater than M is considered as dangerous. Also, any position of the city with y ordinate negative or greater than N is considered as dangerous. You will be given the total sequence of Rakesh's movement. You need to determine if Rakesh ended up being at his relative's house, at a dangerous place, or at a random place in the city.

To make things clear,

-  U indicates a move that increases position along y-axis by 1 
-  D indicates a move that decreases position along y-axis by 1 
-  R indicates a move that increases position along x-axis by 1 
-  L indicates a move that decreases position along x-axis by 1 

Note that we are interested in the position of Rakesh at the end of his journey only. He may visit some dangerous place or his relative's house at some intermediate point but that won't affect the answer.

-----Input-----
- The first line of the input contains an integer T denoting the number of test cases. The description of each test case follows.

- The first line of each test case contains two integers M and N.
- The second line contains two integers Rx and Ry.
- The third line contains the length of Rakesh's move sequence.
- The next line contains the move sequence containing letters U, D, R, and L only with no space.

-----Output-----
For each test case, print "Case i: ", and then the answer, where i is the testcase number, 1-indexed. The answer should be any of the following three strings:
-  "REACHED" if Rakesh could reach his relative's house 
-  "DANGER" if Rakesh ended up being in a dangerous place 
-  "SOMEWHERE" if Rakesh ended up being in somewhere safe place in the city other than his relative's place 
Don't print any quotation mark. Check the sample output.

-----Constraints-----

- 1 ≤ T ≤ 10
- 0 ≤ M, N ≤ 10000
- 0 ≤ Rx ≤  M 
- 0 ≤ Ry ≤  N 
- 0 ≤ Sum of the lengths of all sequences ≤ 10000

-----Example-----
Input:
2
20 20
4 5
13
LLUUUUURRRRRR
10 10
3 4
7
UDUDDRR

Output:
Case 1: REACHED
Case 2: DANGER
user: Two friends David and Rojer were preparing for their weekly class-test.
The are preparing for the math test, but because of continuously adding big integers and solving equations they got exhausted. They decided to take break and play a game. They play a game which will help them in both(for having fun and will also help to prepare for math test).
There are N words and they have to find RESULT with the help of these words (just like they have N integers and they have to find integer RESULT=sum of N integers) . Since they are playing this game for the first time! They are not too good in this. Help them in finding weather their RESULT is correct or not.   
NOTE:- Total number of unique characters in N words are not greater than 10. All input words and RESULT are in UPPER-CASE only!
Refer Here for how to add numbers : https://en.wikipedia.org/wiki/Verbal_arithmetic

-----Input:-----
- First line consist of an integer N (total number of words).
- Next N line contains words with which they have to find RESULT.
- Last line consist of the RESULT they found.

-----Output:-----
If RESULT is correct print true else print false.

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

THIS

IS

TOO

FUNNY  

-----Sample Output:-----
true

-----Constraints-----
- $2 \leq N \leq 10$
- $1 \leq Length of The word \leq 10$
- $1 \leq Length of The Result \leq 11$
user: Today Chef wants to evaluate the dishes of his $N$ students. He asks each one to cook a dish and present it to him.
Chef loves his secret ingredient, and only likes dishes with at least $X$ grams of it.
Given $N$, $X$ and the amount of secret ingredient used by each student $A_i$, find out whether Chef will like at least one dish. 

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- The first line of each testcase contains two integers $N$ 
(number of students) and $X$ (minimum amount of secret ingredient that a dish must contain for Chef to like it).
- The next line contains $N$ space separated integers, $A_i$ denoting the amount of secret ingredient used by the students in their dishes.

-----Output:-----
For each testcase, print a single string "YES" if Chef likes at least one dish. Otherwise, print "NO". (Without quotes).

-----Constraints:-----
- $1 \leq T \leq 100$
- $1 \leq N \leq 1000$
- $1 \leq X \leq 1000000$
- $1 \leq A_i \leq 1000000$

-----Sample Input:-----
3
5 100
11 22 33 44 55
5 50
10 20 30 40 50
5 45
12 24 36 48 60

-----Sample Output:-----
NO
YES
YES
user: Chef has an array A = (A1, A2, ..., AN), which has N integers in it initially. Chef found that for i ≥ 1, if Ai > 0, Ai+1 > 0, and Ai+2 exists, then he can decrease both Ai, and Ai+1 by one and increase Ai+2 by one. If Ai+2 doesn't exist, but Ai > 0, and Ai+1 > 0, then he can decrease both Ai, and Ai+1 (which will be the currently last two elements of the array) by one and add a new element at the end, whose value is 1.
Now Chef wants to know the number of different arrays that he can make from A using this operation as many times as he wishes. Help him find this, and because the answer could be very large, he is fine with you reporting the answer modulo 109+7.
Two arrays are same if they have the same number of elements and if each corresponding element is the same. For example arrays (2,1,1) and (1,1,2) are different. 

-----Input-----
- The first line of the input contains a single integer T denoting the number of test cases.
- The first line contains a single integer N denoting the initial number of elements in A.
- The second line contains N space-separated integers: A1, A2, ... , AN. 

-----Output-----
For each test case, output answer modulo 109+7 in a single line. 

-----Constraints-----
- 1 ≤ T ≤ 5
- 1 ≤ N ≤ 50
- 0 ≤ Ai ≤ 50

-----Subtasks-----
- Subtask 1 (20 points) : 1 ≤ N ≤ 8, 0 ≤ Ai ≤ 4
- Subtask 2 (80 points) : Original constraints

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

Output:
9
4
9

-----Explanation-----
Example case 1.
We'll list the various single steps that you can take (ie. in one single usage of the operation):
- (2, 3, 1) → (2, 2, 0, 1)
- (2, 2, 0, 1) → (1, 1, 1, 1)
- (1, 1, 1, 1) → (1, 1, 0, 0, 1)
- (1, 1, 0, 0, 1) → (0, 0, 1, 0, 1)
- (1, 1, 1, 1) → (1, 0, 0, 2)
- (1, 1, 1, 1) → (0, 0, 2, 1)
- (2, 3, 1) → (1, 2, 2)
- (1, 2, 2) → (0, 1, 3)

So all the arrays you can possibly get are: 
(2, 3, 1), (2, 2, 0, 1), (1, 1, 1, 1), (1, 1, 0, 0, 1), (0, 0, 1, 0, 1), (1, 0, 0, 2), (0, 0, 2, 1), (1, 2, 2), and (0, 1, 3)
Since there are 9 different arrays that you can reach, the answer is 9.
user: Richik$Richik$ has just completed his engineering and has got a job in one of the firms at Sabrina$Sabrina$ which is ranked among the top seven islands in the world in terms of the pay scale. 
Since Richik$Richik$ has to travel a lot to reach the firm, the owner assigns him a number X$X$, and asks him to come to work only on the day which is a multiple of X$X$. Richik joins the firm on 1-st day but starts working from X-th day. Richik$Richik$ is paid exactly the same amount in Dollars as the day number. For example, if Richik$Richik$ has been assigned X=3$X = 3$, then he will be paid 3$3$ dollars and 6$6$ dollars on the 3rd$3rd$ and 6th$6th$ day on which he comes for work. 
On N−th$N-th$ day, the owner calls up Richik$Richik$ and asks him not to come to his firm anymore. Hence Richik$Richik$ demands his salary of all his working days together. Since it will take a lot of time to add, Richik$Richik$ asks help from people around him, let's see if you can help him out. 

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

-----Output:-----
For each testcase, output in a single line which is the salary which Richik$Richik$ demands. 

-----Constraints-----
- 1≤T≤1000$1 \leq T \leq 1000$
- 1≤X<=N≤107$1 \leq X<=N \leq 10^7$

-----Sample Input:-----
1
3 10

-----Sample Output:-----
18
user: You have found $M$ different types of jewels in a mine and each type of jewel is present in an infinite number.
There are $N$ different boxes located at position $(1 ,2 ,3 ,...N)$.
Each box can collect jewels up to a certain number ( box at position $i$ have $i$ different partitions and each partition can collect at most one jewel of any type).
Boxes at odd positions are already fully filled with jewels while boxes at even positions are completely empty.
Print the total number of different arrangements possible so that all boxes can be fully filled.
As the answer can be very large you can print it by doing modulo with 1000000007(10^9+7).

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

-----Output:-----
For each testcase, Print the total number of different arrangement.

-----Constraints-----
- $1 \leq T \leq 20000$
- $1 \leq N \leq 1e9$
- $1 \leq M \leq 1e14$

-----Sample Input:-----
2
1 10
5 2

-----Sample Output:-----
1
64
user: Lets wish Horsbug98 on his birthday and jump right into the question.
In Chefland, $6$ new mobile brands have appeared each providing a range of smartphones. For simplicity let the brands be represented by numbers $1$ to $6$. All phones are sold at the superstore. 
There are total $N$ smartphones. Let $P_i$ & $B_i$ be the price and the brand of the $i^{th}$ smartphone. The superstore knows all the price and brand details beforehand. 
Each customer has a preference for brands. The preference is a subset of the brands available (i.e $1$ to $6$). Also, the customer will buy the $K^{th}$ costliest phone among all the phones of his preference.
You will be asked $Q$ queries. Each query consists of the preference of the customer and $K$.
Find the price the customer has to pay for his preference. If no such phone is available, print $-1$
Note that for each query the total number of smartphones is always $N$ since, after each purchase, the phones are replaced instantly.

-----Input:-----
- First Line contains $N$ and $Q$
- Second-line contains $N$ integers $P_1,P_2,...,P_N$ (Price)
- Third line contains $N$ integers $B_1,B_2,...,B_N$ (Brand)
- Each of the next Q lines contains a query, the query is describes below
- First line of each quey contains $b$ and $K$ where $b$ is the size of the preference subset.
- Second line of each query contains $b$ integers, describing the preference subset.

-----Output:-----
For each query, print the price to be paid.

-----Constraints-----
- $1 \leq N, Q, P_i \leq 10^5$
- $1 \leq B_i, b \leq 6$
- $1 \leq K \leq N$

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

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

-1

-----Explaination-----
Query 1: The preference subset is {1, 2, 3}, The prices of phones available of these brands are {4, 5, 6}. The third costliest phone is 4.
Query 2: The preference subset is {4, 5, 6}, The prices of phones available of these brands are {7}.
Fouth costliest phone is required, which is not available. Hence, answer is $-1$.
user: Chef played an interesting game yesterday. This game is played with two variables $X$ and $Y$; initially, $X = Y = 0$. Chef may make an arbitrary number of moves (including zero). In each move, he must perform the following process:
- Choose any positive integer $P$ such that $P \cdot P > Y$.
- Change $X$ to $P$.
- Add $P \cdot P$ to $Y$.
Unfortunately, Chef has a bad memory and he has forgotten the moves he made. He only remembers the value of $X$ after the game finished; let's denote it by $X_f$. Can you tell him the maximum possible number of moves he could have made in the game?

-----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 integer $X_f$.

-----Output-----
For each test case, print a single line containing one integer — the maximum number of moves Chef could have made.

-----Constraints-----
- $1 \le T \le 10^5$
- $1 \le X_f \le 10^9$

-----Example Input-----
3
3
8
9

-----Example Output-----
3
5
6

-----Explanation-----
Example case 2: One possible sequence of values of $X$ is $0 \rightarrow 1 \rightarrow 2 \rightarrow 3 \rightarrow 5 \rightarrow 8$.
user: The EEE classes are so boring that the students play games rather than paying attention during the lectures. Harsha and Dubey are playing one such game.

The game involves counting the number of anagramic pairs of a given string (you can read about anagrams from here). Right now Harsha is winning. Write a program to help Dubey count this number quickly and win the game!

-----Input-----
The first line has an integer T which is the number of strings. Next T lines each contain a strings. Each string consists of lowercase english alphabets only.

-----Output-----
For each string, print the answer in a newline.

-----Constraints-----
- 1 ≤ T ≤ 1000
- 1 ≤ length of each string ≤ 100

-----Example-----
Input:
3
rama
abba
abcd
Output:
2
4
0

-----Explanation-----
rama has the following substrings:

- r
- ra
- ram
- rama
- a
- am
- ama
- m
- ma
- a
Out of these, {5,10} and {6,9} are anagramic pairs.

Hence the answer is 2.

Similarly for other strings as well.