meetforever/GRPO_CL huggingface dataset:
user: Chef Hari has got a new obsession now: he has started playing chess (read about it here) and he is liking this game very much. Since Hari has spent several months playing chess with his friends, he has now decided to take part in some chess tournament in Cheftown.

There are currently two tournaments going on in Cheftown and each tournament has its own entry fee. Due to this economical restriction and his budget, Hari can take part in only one tournament.

The entry fee for first tournament is F1 units of money. The structure of tournament is as follows: first there will be group matches and then there will be finals. If Hari reaches in finals and wins it, he'll get R1 units of money. If after reaching in finals, Hari loses, he'll get R2 units of money. If Hari fails to reach in finals, he'll get nothing. The probability of reaching in finals of first tournament for Hari is p1 and probability of winning in finals after reaching is p2.

The entry fee for second tournament is F2 units of money. The structure of tournament is as follows: first there will be group matches and then there will be finals. If Hari reaches in finals, he'll immediately get R3 units of money, otherwise he'll get nothing. If after reaching in finals, Hari wins, he'll get R4 units of money. The probability of reaching in finals of second tournament for Hari is p3 and probability of winning in finals after reaching is p4.

Now, Hari wants to maximise his profit. He wants to know which tournament he should participate in such that his expected profit is maximised. Help Hari in deciding this.

Note:
In the tournaments of Cheftown, the game never ends with a draw. So, either Hari wins a game, or he loses.

-----Input-----

First line of the input contains T, the number of test cases. The description of each test case is as following:

First line of each test case contains 6 integers F1, F2, R1, R2, R3 and R4.

Next line of each test case contains 4 floating point numbers p1, p2, p3 and p4.
Each number has exactly 2 digits after decimal point.

-----Output-----

For each test case, output a single line having "FIRST" if expected profit of first tournament is maximum or "SECOND" if expected profit of second tournament is maximum or "BOTH" if expected profits of both the tournaments is exactly same.

-----Constraints-----
- 1 ≤ T ≤ 100
- 1 ≤ F1, F2, R1, R2, R3, R4 ≤ 100
- 0.00 ≤ p1, p2, p3, p4 ≤ 1.00

-----Subtasks-----
Subtask#1: 30 points
- p1 = p3 and p2 = p4

Subtask#2: 70 points
- All usual constraints.

-----Example-----
Input:
2
30 50 70 10 40 30
0.25 0.10 0.30 0.05
50 36 80 38 65 32
0.55 0.12 0.33 0.54

Output:
FIRST
SECOND

-----Explanation-----

In the first case, the expected profit for first tournament is -26.00 and expected profit for second tournament is -37.55. So, first tournament has better expected profit.

In the second case, the expected profit for first tournament is -26.328 and expected profit for second tournament is -8.8476. So, second tournament has better expected profit.
user: -----Problem description.-----
This problem deals with the I/O methods used in codechef. 
You are supposed to print the integer in its reverse form , or in simple words, print the reverse of the given integer . For instance , reverse of  120 is 21  (not 021)  .

-----Input-----
- The first line of each test case contains an integer T .

- following T lines contains distinct integers N .



-----Output-----
- Output should contain T line , each line with the distinct integer as asked in question . 

-----Constraints-----
- 1 ≤ T ≤ 105

- 1 ≤ N ≤ 1018

Subtask 1 :  N ≤ 105
Subtask 2 :  N ≤ 109
Subtask 3 :  N ≤ 1018



-----Example-----
Input:
3
1234
4567
1

Output:
4321
7654
1

-----Explanation-----
reverse of 1234 is 4321 , 4567 is 7654 & of 1 is 1 

NOTE: testcases may contain large range of data, use datatypes accordingly .
user: Salmon loves to be a tidy person. One day, when he looked at the mess that he made after playing with his rubber ducks, he felt awful. Now he wants to clean up his mess, by placing his ducks into boxes.
Each rubber duck has a color. There are a total of $N+1$ colors, numbered from $0$ to $N$. Salmon wants to place his $N*K$ ducks into $N$ boxes, each of which can fit $K$ ducks. Each duck should be placed inside a box.
Salmon is very particular when it comes to how many colors he can place in each box. Since Salmon doesn't like lots of colors mixing together he only wants to have a maximum of $2$ distinct colors per box.
Please help Salmon achieve this goal!

It can be shown that there will always be at least one valid solution under given constraints.

If there are multiple correct solutions, you may output any one of them.   

-----Input:-----
- The first line contains an integer $T$, denoting the number of testcases. $T$ testcases will follow, each containing two lines.   
- The first line of each testcase contains two space-separated integers $N$ and $K$.   
- The second line of each testcase contains $N+1$  space-separated integers. The $i+1$-th integer denotes the number of ducks with color-$i$ where $0 \leq i \leq N$

-----Output:-----
- Output $N$ lines for each testcase. 
- The $i$-th line of a testcase should contain $4$ space-separated integers $c1, m1, c2, m2$ respectively which denotes that that are $m1$ ducks of color-$c1$ and $m2$ ducks of color-$c2$ inside the $i$-th box where $0 \leq m1,m2 \leq K$ and $0 \leq c1,c2 \leq N$. 
- Note that even if you have only one color to put inside the $i$-th box, you should still output $4$ space-separated integers and keep either $m1$ or $m2$ as $0$. And $0 \leq c1,c2 \leq N$.
- The output should be valid and should satisfy Salmon's goal.

-----Constraints-----
- $T=10$
- $2 \leq N \leq 10^5$ 
- $2 \leq K \leq 10^5$ 
- Total ducks for each test case is exactly $N*K$
- There can be a color with $0$ ducks

-----Subtasks-----
- Subtask 1 [20 points]: $2 \leq N \leq 10$, $K=2$ 
- Subtask 2 [30 points]: $N=2$, $K=5$
- Subtask 3 [50 points]: original constraints

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

-----Sample Output:-----
2 1 1 3
1 1 0 3

-----Explanation:-----
- In the given testcase, Salmon has $N=2$ boxes, each of size $K=4$ and there are total $N*K=8$ ducks.   
- The first box is filled with $1$ duck of color-$2$ and $3$ ducks of color-$1$ and the second box is filled with $1$ duck of color-$1$ and $3$ ducks of color-$0$.   
- Each duck is inside a box and each box has at most two distinct colors. Also each box contains exactly $K=4$ ducks.
user: -----General Statement:-----
Given the actual high and low temperatures for the day and the normal high and low temperatures for that day, calculate the average difference from normal.

-----Input:-----
The first line of the data set for this problem is an integer that represents the number of data sets that follow. Each data set is on a separate line and consists of today’s high, today’s low, normal high, and normal low – in that order.

-----Output:-----
If the average difference is negative, do not output the negative sign (-).
Output the amount of deviation from normal, followed by the words
DEGREE(S) ABOVE NORMAL, or by the words
DEGREE(S) BELOW NORMAL.
Round to 1 decimal place. A trailing zero is required if the average is an integer.
The output is to be formatted exactly like that for the sample output given below.

-----Assumptions:-----
Temperatures are in the range –15..100 degrees.
The average temperature difference will not be zero.

-----Discussion:-----
Determine the average of the difference of the high temperatures and the difference of the low temperatures.

-----Sample Input:-----
3
75 45 78 40
50 32 45 30
56 48 62 45

-----Sample Output:-----
1.0 DEGREE(S) ABOVE NORMAL
3.5 DEGREE(S) ABOVE NORMAL
1.5 DEGREE(S) BELOW NORMAL
user: There are K nuclear reactor chambers labelled from 0 to K-1. Particles are bombarded onto chamber 0. The particles keep collecting in the chamber 0. However if at any time, there are more than N particles in a chamber, a reaction will cause 1 particle to move to the immediate next chamber(if current chamber is 0, then to chamber number 1), and all the particles in the current    chamber will be be destroyed and same continues till no chamber has number of particles greater than N. Given K,N and the total number of particles bombarded (A), find the final distribution of particles in the K chambers. Particles are bombarded one at a time. After one particle is bombarded, the set of reactions, as described, take place. After all reactions are over, the next particle is bombarded. If a particle is going out from the last chamber, it has nowhere to go and is lost.

-----Input-----

The input will consist of one line containing three numbers A,N and K separated by spaces.
A will be between 0 and 1000000000 inclusive.
N will be between 0 and 100 inclusive.
K will be between 1 and 100 inclusive.
All chambers start off with zero particles initially.

-----Output-----

Consists of K numbers on one line followed by a newline. The first number is the number of particles in chamber 0, the second number is the number of particles in chamber 1 and so on.

-----Example-----
Input:
3 1 3
Output:
1 1 0
Explanation
Total of 3 particles are bombarded. After particle 1 is bombarded, the chambers have particle distribution as
"1 0 0". After second particle is bombarded, number of particles in chamber 0 becomes 2 which is greater
than 1. So, num of particles in chamber 0 becomes 0 and in chamber 1 becomes 1. So now distribution is
"0 1 0". After the 3rd particle is bombarded, chamber 0 gets 1 particle and so distribution is "1 1 0" after all
particles are bombarded one by one.
user: A simple string contains a large repetition of letters within it. This problem is related to string handling and manipulation.  An original message is sent from planet Earth to planet Cybertron in form of a string. However, the letter position and string size is not important. The number of time each letter has occurred in the string is important. So the original string which is sent to Cybertron is encrypted in the new string which comprises the letters followed by each time it has occurred in the original string. Eg- original message is- abcdabf. Then the encrypted string is- a2b2c1d1f1

-----Input-----
The input consists of a single line string without any space or numeric or special characters.

-----Output-----
It will consist of in the encrypted string which comprises the letters followed by each time it has occurred in the original string in order.

-----Example-----
Input:
information

Output:
i2n2f1o2r1m1a1t1
user: The chef was searching for his pen in the garage but he found his old machine with a display and some numbers on it. If some numbers entered then some different output occurs on the display. Chef wants to crack the algorithm that the machine is following.
Example to identify the pattern :
Input                            Output
9                                   36
5                                   10
1                                    0
2                                    1

-----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, $N$. 

-----Output:-----
For each test case, output in a single line answer as displayed on the screen.

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

-----Sample Input:-----
1
7

-----Sample Output:-----
21
user: Chef works as a cook in a restaurant. Each morning, he has to drive down a straight road with length K$K$ to reach the restaurant from his home. Let's describe this road using a coordinate X$X$; the position of Chef's home is X=0$X = 0$ and the position of the restaurant is X=K$X = K$.
The road has exactly two lanes (numbered 1$1$ and 2$2$), but there are N$N$ obstacles (numbered 1$1$ through N$N$) on it. For each valid i$i$, the i$i$-th obstacle blocks the lane Li$L_i$ at the position X=Xi$X = X_i$ and does not block the other lane.
When driving, Chef cannot pass through an obstacle. He can switch lanes in zero time at any integer X$X$-coordinate which does not coincide with the X$X$-coordinate of any obstacle. However, whenever he switches lanes, he cannot switch again until driving for at least D$D$ units of distance, and he can travel only in the direction of increasing X$X$. Chef can start driving in any lane he wants. He can not switch lanes at non-integer  X$X$-coordinate.
Sometimes, it is impossible to reach the restaurant without stopping at an obstacle. Find the maximum possible distance Chef can travel before he has to reach an obstacle which is in the same lane as him. If he can avoid all obstacles and reach the restaurant, the answer is K$K$.

-----Input-----
- The first line of the input contains a single integer T$T$ denoting the number of test cases. The description of T$T$ test cases follows.
- The first line of each test case contains three space-separated integers N$N$, K$K$ and D$D$.
- The second line contains N$N$ space-separated integers X1,X2,…,XN$X_1, X_2, \ldots, X_N$.
- The third line contains N$N$ space-separated integers L1,L2,…,LN$L_1, L_2, \ldots, L_N$.

-----Output-----
For each test case, print a single line containing one integer ― the maximum distance Chef can travel.

-----Constraints-----
- 1≤T≤1,000$1 \le T \le 1,000$
- 1≤N≤105$1 \le N \le 10^5$
- 2≤K≤109$2 \le K \le 10^9$
- 1≤D≤109$1 \le D \le 10^9$
- 1≤Xi≤K−1$1 \le X_i \le K-1$ for each valid i$i$
- Xi<Xi+1$X_i < X_{i+1}$ for each valid i$i$
- 1≤Li≤2$1 \le L_i \le 2$ for each valid i$i$
- the sum of N$N$ over all test cases does not exceed 106$10^6$

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

-----Example Input-----
4
2 10 20
4 7
1 2
4 15 20
4 6 9 13
1 2 2 1
5 10 1
1 3 5 7 9
1 2 1 2 1
2 10 2
4 5
1 2

-----Example Output-----
10
13
10
5

-----Explanation-----
Example case 1: Chef can start in lane 2$2$ and switch to lane 1$1$ at the position X=6$X = 6$, then continue until reaching the restaurant.
Example case 2: Chef can start in lane 2$2$ and switch to lane 1$1$ at X=5$X = 5$. However, he cannot avoid the obstacle at X=13$X = 13$, because he has not driven for at least 20$20$ units since the last switch.
Example case 3: Chef should start in lane 2$2$ and then switch lanes at the positions X=2$X=2$, X=4$X=4$, X=6$X=6$ and X=8$X=8$. This way, he can reach the restaurant.
Example case 4: Chef can start in lane 2$2$ but he cannot escape the second obstacle at X$X$=5 since the first obstacle at X$X$=4 doesn't give enough space for Chef to switch lanes.
user: Chef has an array of N integers. He wants to play a special game. In this game he needs to make all the integers in the array greater than or equal to 0. 
Chef can use two types of operations. The first type is to  increase all the integers of the given array by 1, but it costs X coins. The operation of the second type is to add 1 to only one integer of the given array and to use this operation you need to pay 1 coin. You need to calculate the minimal cost to win this game (to make all integers greater than or equal to 0)  

-----Input-----

The first line of the input contains an integer N denoting the number of elements in the given array. The second line contains N space-separated integers A1, A2, ..., AN denoting the given array. The third line contains number X - cost of the first type operation. 


-----Output-----
For each test case, output a single line containing minimal cost required to make all the integers greater than or equal to zero.

-----Constraints-----

- 1 ≤ N ≤ 105
- -109 ≤ Ai ≤  109 
- 0 ≤ X  ≤ 109

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

Output:
5

-----Explanation-----
Example case 1: Use the first type operation twice and the second type once.
user: Due to COVID19 all employees of chemical factory are quarantined in home. So, company is organized by automated robots. There are $N$ Containers in company, which are labelled with $1$ to $N$ numbers. There are Total $N$ robots in Company, which are labelled $1$ to $N$. 
Each Robot adds $1$ litter Chemical in containers whose labels are multiple of robots’ label. (E.g. robot labelled 2 will add Chemical in containers labelled 2, 4, 6, ….). 
Robots follow few rules mentioned below:
- Chemical with $pH<7$ is acidic.
- Chemical with $pH=7$ is neutral.
- Chemical with $pH>7$ is basic.
- Mixture of $1$ litter acid and $1$ litter base makes neutral solution.
- If Container is empty or pH of Chemical in container is equal to 
- $7$ then robot adds $1$ litter acidic Chemical.
- If pH of Chemical in container is less than $7$ then robots adds $1$ litter basic Chemical.
Now Chemical is packed in $4$ ways:
- Containers with exactly $2$ litter acid and $1$ litter base are packed at $P1$ cost. 
- Containers with acidic Chemical are packed at $P2$ cost. (Here Don’t consider containers with exactly $2$ litter acid and $1$ litter base as we counted them in above rule)
- Containers with $pH=7$ Chemical is packed at $P3$ cost.
- Containers with Basic Chemical are packed at $P4$ cost.
Now $1$ employee given task to find packing cost of containers with labels in range $[ k1, k2]$ (Inclusive). Help him out. As Cost can be large find cost in modulo of $100000007$

-----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 $3$ space separated Integers $N$, $K1$ and $K2$.
- The second and last line contains $4$ space separated Integers $P1$, $P2$, $P3$ and $P4$

-----Output:-----
For each test case, print total cost of packing of containers modulo 100000007.

-----Constraints-----
- $1 \leq T \leq 50000$
- $1 \leq P1, P2, P3, P4 \leq 2*10^7$
- $2 \leq N \leq 2*10^7$
- $1 \leq K1, K2 \leq N$

-----Subtasks-----Subtask #1 (20 points):
- $1 \leq T \leq 10$
- $1 \leq P1, P2, P3, P4 \leq 2*10^7$
- $2 \leq N \leq 1000$
- $1 \leq K1, K2 \leq N$Subtask #2 (80 points) :
- Original Constraint

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

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

-----Explanation:-----
Let’s use notation, 
0 for acidic Chemical, 
1 for Chemical with pH=7, 
2 for basic Chemical,
3 for Containers with exactly 2 litter acid and 1 litter base,
-1 for empty containers
Initially 4 containers are empty so
[-1, -1, -1, -1]
Robot 1 adds 1 litter acid in all containers.
[0, 0, 0, 0]
Robot 2 adds base in containers labelled 2, 4
[0, 1, 0, 1]
Robot 3 adds base in containers labelled 3
[0, 1, 1, 1]
Robot 4 adds acid in containers labelled 4 because it contains Chemical with pH=7. After adding acid, it also contains exactly 2 litter acid and 1 litter base, so denoting it with 3.
[0, 1, 1, 3]
Corresponding cost of packing container
[P2, P3, P3, P1]
Now, calculate total cost,
Cost = P2+P3+P3+P1 = 2+2+2+2 = 8
user: On each of the following $N$ days (numbered $1$ through $N$), Chef is planning to cook either pizza or broccoli. He wrote down a string $A$ with length $N$, where for each valid $i$, if the character $A_i$ is '1', then he will cook pizza on the $i$-th day, while if $A_i$ is '0', he will cook broccoli on this day.
Chefu, his son, loves pizza but hates broccoli ― just like most kids. He wants to select a substring of $A$ with length $K$ and change each character '0' in this substring to '1'. Afterwards, let's define pizza time as the maximum number of consecutive days where Chef will cook pizza. Find the maximum pizza time Chefu can achieve.

-----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 a string $A$ with length $N$.

-----Output-----
For each test case, print a single line containing one integer ― the maximum pizza time.

-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le K \le N \le 10^5$
- $A$ contains only characters '0' and '1'
- the sum of $N$ over all test cases does not exceed $10^6$

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

-----Example Input-----
2
13 2
0101110000101
6 3
100001

-----Example Output-----
5
4

-----Explanation-----
Example case 1: Chefu can choose the substring $A[2, 3]$ = "10", and change the third character of $A$ to '1'. Then, the pizza time is $5$ days: from day $2$ to day $6$.
Example case 2: Chefu can choose the substring $A[2, 4]$ = "000". Then, the pizza time is $4$ days: from day $1$ to day $4$.
user: Gru has a string $S$ of length $N$, consisting of only characters $a$ and $b$ for banana and $P$ points to spend.
Now Gru wants to replace and/or re-arrange characters of this given string to get the lexicographically smallest string possible. For this, he can perform the following two operations any number of times.
1) Swap any two characters in the string. This operation costs $1$ $point$. (any two, need not be adjacent)
2) Replace a character in the string with any other lower case english letter. This operation costs $2$ $points$.
Help Gru in obtaining the lexicographically smallest string possible, by using at most $P$ points.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains two lines of input, first-line containing two integers $N$ , $P$.
- The second line contains a string $S$ consisting of $N$ characters.

-----Output:-----
For each testcase, output in a single containing the lexicographically smallest string obtained.

-----Constraints-----
- $1 \leq T \leq 10$
- $1 \leq N \leq 10^5$
- $0 \leq P \leq 2N$
- $S$ only consists of $'a'$ and $'b'$

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

-----Sample Output:-----
aab

-----Explanation:-----
We swap $S[0]$ and $S[2]$, to get $abb$. With the 2 remaining points, we replace $S[1]$ to obtain $aab$ which is the lexicographically smallest string possible for this case.
user: -----Problem description-----
As a holiday gift, Tojo received a probability problem. The problem read as follows
Consider an N by M grid. Rows are numbered 1 to N, from top to bottom. Columns are numbered 1 to M, from left to right. You are initially at cell (1, 1) and want to go to cell (N, M). From any cell you can move to the cell below it or to the cell right to it. You should never go out of the grid. At any point you should consider all the possibilities of movement with equal probability
Let P[i][j] be the probability of visiting cell (i, j). You need to calculate the sum of P[i][j] for 1 ≤ i ≤ N, 1 ≤ i ≤ M.
As we all know, Tojo really hates probability related problems. He wants you to solve this task

-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.Only line of each test case has two integer N and M.

-----Output-----
For each test case, output a single line containing the required answer. Answers within an absolute or relative error of 10-6 will be accepted.

-----Constraints-----
- 1 ≤ T ≤ 1000
- 1 ≤ N ≤ 1000
- 1 ≤ M ≤ 1000

-----Example-----
Input:
2
2 2
1 6

Output:
3.000000
6.000000

-----Explanation-----
Example case 1
Probability matrix P for N=2, M=2 is

1.0 0.5

0.5 1.0

You are at (1, 1) initially. So the probablity of visiting (1, 1) is 1. At (1, 1) you have 2 options, move below to (2, 1) or to right cell (1, 2). Probablity of going to (1, 2) is 0.5. Probability of going to (2, 1) is 0.5. You always end up at (2, 2), so P[2][2] is 1. Required sum = 1.0 + 0.5 + 0.5 + 1.0 = 3.0
Example case 2
Probability matrix P for N=1, M=6 is

1.0 1.0 1.0 1.0 1.0 1.0

Because at any position there is only one possible next position.