meetforever/GRPO_CL huggingface dataset:
user: -----Problem Statement-----
Chef studies combinatorics. He tries to group objects by their rang (a positive integer associated with each object). He also gives the formula for calculating the number of different objects with rang N as following:

the number of different objects with rang N = F(N) = A0 + A1 * N + A2 * N2 + A3 * N3.

Now Chef wants to know how many different multisets of these objects exist such that sum of rangs of the objects in the multiset equals to S. You are given the coefficients in F(N) and the target sum S. Please, find the number of different multisets modulo 1,000,000,007.

You should consider a multiset as an unordered sequence of integers. Two multisets are different if and only if there at least exists one element which occurs X times in the first multiset but Y times in the second one, where (X ≠ Y).

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

The first line of each test case contains four integers A0, A1, A2, A3. The second line contains an integer S.

-----Output-----
For each test case, output a single line containing a single integer - the answer to the test case modulo 1,000,000,007.

-----Constraints-----
- 1 ≤ T ≤ 500
- 1 ≤ S ≤ 100
- 0 ≤ Ai ≤ 1000
- Sum of all S for all test cases is not greater than 500. It's guaranteed that at least one Ai is non-zero.

-----Example-----
Input:
4
1 0 0 0
1
1 0 0 0
3
0 1 0 0
2
2 3 1 4
10

Output:
1
3
3
213986343

-----Explanation-----
Example case 2. 

In the second example function looks as follows F(N) = 1. So for each rang there is a single object of the rang. To get multiset with sum of rangs equal to 3, you can pick: three objects of rang 1, or one object of rang 1 and one of rang 2, or only one object of rang 3. 
Example case 3. 

In the third example function looks as follows F(N) = N. So, you have one distinct object of rang 1, two distinct objects of rang 2, three distinct objects of rang 3 and so on. To get
multiset with sum of rangs equal to 2, you can pick: two objects of rang 1, one of objects of rang 2 (two ways).
user: In India, every individual is charged with income tax on the total income each year. This tax is applied to specific ranges of income, which are called income tax slabs. The slabs of income tax keep changing from year to year. This fiscal year (2020-21), the tax slabs and their respective tax rates are as follows:Total income (in rupees)Tax rateup to Rs. 250,0000%from Rs. 250,001 to Rs. 500,0005%from Rs. 500,001 to Rs. 750,00010%from Rs. 750,001 to Rs. 1,000,00015%from Rs. 1,000,001 to Rs. 1,250,00020%from Rs. 1,250,001 to Rs. 1,500,00025%above Rs. 1,500,00030%
See the sample explanation for details on how the income tax is calculated.
You are given Chef's total income: $N$ rupees (Rs.). Find his net income. The net income is calculated by subtracting the total tax (also called tax reduction) from the total income. Note that you do not need to worry about any other kind of tax reductions, only the one described above.

-----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 $N$.

-----Output-----
For each test case, print a single line containing one integer — Chef's net income.

-----Constraints-----
- $1 \le T \le 10^3$
- $0 \le N \le 10^7$
- $N$ is a multiple of $100$

-----Example Input-----
2
600000
250000

-----Example Output-----
577500
250000

-----Explanation-----
Example case 1: We know that the total income is Rs. $6$ lakh ($1$ lakh rupees = $10^5$ rupees). The total tax for each slab is calculated as follows:
- Up to $2.5$ lakh, the tax is Rs. $0$, since the tax rate is $0$ percent.
- From above Rs. $2.5$ lakh to Rs. $5$ lakh, the tax rate is $5$ percent. Therefore, this tax is $0.05 \cdot (500,000-250,000)$, which is Rs. $12,500$.
- From above Rs. $5$ lakh to Rs. $6$ lakh, the tax rate is $10$ percent. Therefore, this tax is $0.10 \cdot (600,000-500,000)$, which is Rs. $10,000$.
- Summing them up, we get that the total tax on Chef's whole income is Rs. $22,500$. Since the net income is the total income minus the tax reduction, it is Rs. $600,000$ minus Rs. $22,500$, which is Rs. $577,500$.
Example case 2: For income up to Rs. $2.5$ lakh, we have no tax, so the net income is the same as the total income: Rs. $2.5$ lakh.
user: In this problem the input will consist of a number of lines of English text consisting of the letters of the English alphabet, the punctuation marks ' (apostrophe), . (full stop), , (comma), ; (semicolon), :(colon) and white space characters (blank, newline). Your task is print the words in the text in reverse order without any punctuation marks.
For example consider the following candidate for the input text:
$ $
This is a sample piece of text to illustrate this 
problem.  If you are smart you will solve this right.

$ $
The corresponding output would read as:
$ $
right this solve will you smart are you If problem
this illustrate to text of piece sample a is This

$ $
That is, the lines are printed in reverse order and in each line the words are printed in reverse order.

-----Input:-----
The first line of input contains a single integer $N$, indicating the number of lines in the input. This is followed by $N$ lines of input text.

-----Output:-----
$N$ lines of output text containing the input lines in reverse order and where each line contains the words in reverse order as illustrated above.

-----Constraints:-----
- $1 \leq N \leq 10000$.
- There are at most $80$ characters in each line

-----Sample input-----
2
This is a sample piece of text to illustrate this 
problem.  If you are smart you will solve this right.

-----Sample output-----
right this solve will you smart are you If problem
this illustrate to text of piece sample a is This
user: Our Chef who was a renouned mathematician has recently got into diamonds' business. 
She has accidentally misplaced $Q$ diamonds into a jar which already had $N$ chocolates. She then started wondering about an interesting question as following. 
If we pick items one by one at random without replacement, what would be the expected number of picks required to get all diamonds out. 

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

-----Output:-----
For each testcase, output the answer in a single line. Your answer is considered if its absolute or relative error doesn't exceed $10^{-6}$

-----Constraints-----
- $1 \leq T \leq 10^5$
- $1 \leq N \leq 10^5$
- $1 \leq Q \leq 10^5$

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

-----Sample Output:-----
3.3333333333

-----EXPLANATION:-----
Here there are 2 Diamonds, 2 chocolates in the jar. 
Say C is chocolate, D is diamond.
If the random order of picking them from left to right is "CDDC", after 3 picks (CDD) all diamonds are out.
Similarly, for the remaining orders it would be the following:
"CDCD" => 4
"CCDD" => 4
"DDCC" => 2
"DCDC" => 3
"DCCD" => 4
Hence the expected number of picks would be (3+4+4+2+3+4)/6 = 3.333333
user: Our chef has recently opened a new restaurant with a unique style. The restaurant is divided into K compartments (numbered from 1 to K) and each compartment can be occupied by at most one customer. 
Each customer that visits the restaurant has a strongly preferred compartment p (1 ≤ p ≤ K), and if that compartment is already occupied, then the customer simply leaves. Now obviously, the chef wants to maximize the total number of customers that dine at his restaurant and so he allows (or disallows) certain customers so as to achieve this task. You are to help him with this. 
Given a list of N customers with their arrival time, departure time and the preferred compartment, you need to calculate the maximum number of customers that can dine at the restaurant. 

-----Input-----
The first line contains an integer T denoting the number of test cases. Each of the next T lines contains two integers N and  K , the number of customers that plan to visit the chef's restaurant and the number of compartments the restaurant is divided into respectively. Each of the next N lines contains three integers si, fi and pi , the arrival time, departure time and the strongly preferred compartment of the ith customer respectively.  

Note that the ith customer wants to occupy the pith compartment from [si, fi)  i.e the ith customer leaves just before   fi  so that another customer can occupy that compartment from   fi  onwards.

-----Output-----
For every test case, print in a single line the maximum number of customers that dine at the restaurant.

-----Constraints-----
-  1 ≤  T ≤   30 
-  0  ≤ N  ≤  105 
-  1  ≤  K  ≤  109 
-  0  ≤  si < fi ≤   109 
-  1  ≤  pi  ≤  K  

-----Example-----
Input:
2
3 3
1 3 1
4 6 2
7 10 3
4 2
10 100 1
100 200 2
150 500 2
200 300 2

Output:
3
3

-----Explanation-----
Example case 1.

All three customers want different compartments and hence all 3 can be accommodated.

Example case 2.

If we serve the 1st, 2nd and 4th customers, then we can get a maximum of 3.
user: Chef and Chefina are best friends. Chefina wants to test the Problem Solving skills of chef so she provides Chef 2 integer number  $X$ and $Y$
The task of chef is to take the  two numbers $X$ and $Y$ and return their SUM.
Identify whether Chef can solve the problem or not? 

-----Input:-----
- First line will contain the two integers $X$ and $Y$.

-----Output:-----
For each testcase, output in a single line the SUM of these two numbers $X$ and $Y$.

-----Constraints-----
- $1 \leq X \leq 100$
- $1 \leq Y \leq 100$

-----Sample Input:-----
6 70

-----Sample Output:-----
76
user: Most problems on CodeChef highlight chef's love for food and cooking but little is known about his love for racing sports. He is an avid Formula 1 fan. He went to watch this year's Indian Grand Prix at New Delhi. He noticed that one segment of the circuit was a long straight road. It was impossible for a car to overtake other cars on this segment. Therefore, a car had to lower down its speed if there was a slower car in front of it. While watching the race, Chef started to wonder how many cars were moving at their maximum speed.
Formally, you're given the maximum speed of N cars in the order they entered the long straight segment of the circuit. Each car prefers to move at its maximum speed. If that's not possible because of the front car being slow, it might have to lower its speed. It still moves at the fastest possible speed while avoiding any collisions. For the purpose of this problem, you can assume that the straight segment is infinitely long.
Count the number of cars which were moving at their maximum speed on the straight segment.

-----Input-----
The first line of the input contains a single integer T denoting the number of test cases to follow. Description of each test case contains 2 lines. The first of these lines contain a single integer N, the number of cars. The second line contains N space separated integers, denoting the maximum speed of the cars in the order they entered the long straight segment.

-----Output-----
For each test case, output a single line containing the number of cars which were moving at their maximum speed on the segment.

-----Example-----
Input:
3
1
10
3
8 3 6
5
4 5 1 2 3

Output:
1
2
2

-----Constraints-----

1 ≤ T ≤ 100

1 ≤ N ≤ 10,000

All speeds are distinct positive integers that fit in a 32 bit signed integer.

Each input file will not be larger than 4 MB (4,000,000,000 bytes) in size.

WARNING! The input files are very large. Use faster I/O.
user: Chef's pizza is the tastiest pizza to exist, and the reason for that is his special, juicy homegrown tomatoes. 
Tomatoes can be grown in rectangular patches of any side lengths. However, Chef only has a limited amount of land. 
Consider the entire town of Chefville to be consisting of cells in a rectangular grid of positive coordinates. 
Chef own all cells (x,y)$(x, y)$ that satisfy x∗y≤N$x*y \leq N$
As an example if N=4$N = 4$, Chef owns the following cells: 
(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(3,1),(4,1)$(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (3, 1), (4, 1) $
Chef can only grow tomatoes in rectangular patches consisting only of cells which belong to him. Also, if he uses a cell, he must use it entirely. He cannot use only a portion of it. 
Help Chef find the number of unique patches of rectangular land that he can grow tomatoes in! Since this number can be very large, output it modulo 1000000007$1000000007$.

-----Input:-----
- The first line of the input contains T$T$, the number of test cases.
- The next T$T$ lines of input contains one integer N$N$.

-----Output:-----
For each testcase, output the number of ways modulo 1000000007$1000000007$.

-----Constraints-----
- 1≤T≤5$1 \leq T \leq 5$
- 1≤N≤1010$1 \leq N \leq 10^{10}$

-----Sample Input:-----
2
4
10000000000

-----Sample Output:-----
23
227374950
user: Ram and Shyam are sitting next to each other, hoping to cheat on an exam. However, the examination board has prepared $p$ different sets of questions (numbered $0$ through $p-1$), which will be distributed to the students in the following way:
- The students are assigned roll numbers — pairwise distinct positive integers.
- If a student's roll number is $r$, this student gets the $((r-1)\%p)$-th set of questions.
Obviously, Ram and Shyam can cheat only if they get the same set of questions.
You are given the roll numbers of Ram and Shyam: $A$ and $B$ respectively. Find the number of values of $p$ for which they can cheat, or determine that there is an infinite number of such values.

-----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 two space-separated integers $A$ and $B$.

-----Output-----
For each test case, print a single line — the number of values of $p$ for which Ram and Shyam can cheat, or $-1$ if there is an infinite number of such values.

-----Constraints-----
- $1 \le T \le 100$
- $1 \le A, B \le 10^8$

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

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

-----Explanation-----
Example case 1: They can cheat for $p = 1$, $p = 2$ or $p = 4$.
user: Mysterious Chefland… Recently, Chef realised that Discuss, the educational system of Chefland, is out of date. Therefore, he is trying to find ways to update the infrastructure in the country. One possible way is to move all materials from Discuss to Discourse.
Chef will have access to Discourse if his knowledge and power become exactly equal to $N$ and $M$ respectively. Initially, he has power $1$ and knowledge $1$.
Chef can perform actions of the following types to improve his skills:
- solve a problem — increase his knowledge by $X$
- do a push-up — increase his power by $Y$
- install ShareChat to keep in touch with friends — increase both knowledge and power by $1$
Chef can only install ShareChat at most once. The remaining actions may be performed any number of times and the actions may be performed in any order.
Help Chef find out whether it is possible to move from Discuss to Discourse.

-----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 four space-separated integers $N$, $M$, $X$ and $Y$.

-----Output-----
For each test case, print a single line containing the string "Chefirnemo" if it is possible to reach the required knowledge and power or "Pofik" if it is impossible.

-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N, M, X, Y \le 10^9$

-----Subtasks-----
Subtask #1 (30 points): $1 \le N, M, X, Y \le 100$
Subtask #2 (70 points): original constraints

-----Example Input-----
5
2 2 1 2
11 10 5 9
11 11 5 9
12 11 5 9
1 2 1 100

-----Example Output-----
Chefirnemo
Chefirnemo
Pofik
Chefirnemo
Pofik

-----Explanation-----
Example case 2: We add $Y=9$ once to the power to get power $10$. We add $X=5$ twice to the knowledge to get knowledge $11$.
Example case 3: We can see that it is impossible to reach power $M=11$ no matter which or how many operations we do. Note that the ShareChat operation will increase both knowledge and power by $1$, and hence it will still be impossible to attain the given values of knowledge and power at the same time.
Example case 4: We can reach knowledge $11$ and power $10$ like in example case 2, the only difference is that we also use the ShareChat operation to increase both by $1$.
user: Chef has a sequence $A_1, A_2, \ldots, A_N$. For a positive integer $M$, sequence $B$ is defined as $B = A*M$ that is, appending $A$ exactly $M$ times. For example, If $A = [1, 2]$ and $M = 3$, then $B = A*M = [1, 2, 1, 2, 1, 2]$
You have to help him to find out the minimum value of $M$ such that the length of the longest strictly increasing subsequence is maximum possible.

-----Input:-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Output:-----
For each test case, print a single line containing one integer ― the minimum value of $M$.

-----Constraints-----
- $1 \le T \le 500$
- $1 \le N \le 2*10^5$
- $1 \le A_i \le 10^9$
- It's guaranteed that the total length of the sequence $A$ in one test file doesn't exceed $2*10^6$

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

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

-----Explanation:-----
In the first test case, Choosing $M = 2$ gives $B = [2, 1, 2, 1]$ which has a longest strictly increasing sequence of length $2$ which is the maximum possible.
In the second test case, Choosing $M = 1$ gives $B  = [1, 2]$ which has a longest strictly increasing sequence of length $2$ which is the maximum possible.
user: You have initially a string of N characters, denoted by A1,A2...AN. You have to print the size of the largest subsequence of string A such that all the characters in that subsequence are distinct ie. no two characters in that subsequence should be same.

A subsequence of string A is a sequence that can be derived from A by deleting some elements  and without changing the order of the remaining elements.

-----Input-----
First line contains T, number of testcases. Each testcase consists of a single string in one line. Each character of the string will be a small alphabet(ie. 'a' to 'z').

-----Output-----
For each testcase, print the required answer in one line.

-----Constraints-----
- 1 ≤ T ≤ 10
- Subtask 1 (20 points):1 ≤ N ≤ 10
- Subtask 2 (80 points):1 ≤ N ≤ 105

-----Example-----
Input:
2
abc
aba

Output:
3
2

-----Explanation-----
For first testcase, the whole string is a subsequence which has all distinct characters.

In second testcase, the we can delete last or first 'a' to get the required subsequence.
user: Recently, Chef found a new formula for computing powers of a sequence:
- You are given two sequences $A_1, A_2, \ldots, A_N$ and $(l_1, r_1), (l_2, r_2), \ldots, (l_N, r_N)$.
- The $1$-st power of the sequence $A$ is $A^1 = A$.
- For each $k > 1$, the $k$-th power of the sequence $A$ (denoted by $A^k$) is a sequence with length $N$ such that for each valid $i$, the $i$-th element of this sequence is (Ak)i=(Ak−1)li⊕(Ak−1)li+1⊕…⊕(Ak−1)ri−1⊕(Ak−1)ri.(Ak)i=(Ak−1)li⊕(Ak−1)li+1⊕…⊕(Ak−1)ri−1⊕(Ak−1)ri.(A^k)_i = (A^{k-1})_{l_i} \oplus (A^{k-1})_{l_i+1} \oplus \ldots \oplus (A^{k-1})_{r_i-1} \oplus (A^{k-1})_{r_i} \,.
After discovering this new formula, Chef tried to find $A^K$, but he felt that it is very time consuming. Therefore, Chef wants you to do it. Can you find the $K$-th power of $A$ for Chef?

-----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 $A_1, A_2, \ldots, A_N$.
- $N$ lines follow. For each valid $i$, the $i$-th of these lines contains two space-separated integers $l_i$ and $r_i$.

-----Output-----
For each test case, print a single line containing $N$ space-separated integers $(A^K)_1, (A^K)_2, \ldots, (A^K)_N$.

-----Constraints-----
- $1 \le T \le 3$
- $1 \le N \le 500$
- $1 \le K \le 5 \cdot 10^7$
- $1 \le A_i \le 10^{18}$ for each valid $i$
- $1 \le l_i \le r_i \le N$ for each valid $i$

-----Subtasks-----
Subtask #1 (50 points):
- $T = 1$
- $N \le 100$
Subtask #2 (50 points): original constraints

-----Sample Input-----
1
3 2
1 2 3
1 2
2 3
1 3

-----Example Ouput-----
3 1 0

-----Explanation-----
Example case 1:
- $(A^2)_1 = A_1 \oplus A_2 = 1 \oplus 2 = 3$
- $(A^2)_2 = A_2 \oplus A_3 = 2 \oplus 3 = 1$
- $(A^2)_3 = A_1 \oplus A_2 \oplus A_3 =1 \oplus 2 \oplus 3 = 0$
user: Chandler has a list of non zero positive integers with him. He made a very interesting observation about the list. He noticed that the number of unique integers in an array of size $N$ is in the range $L$ to $R$ (both inclusive) and every element was either 1 or an even number x, in which case x/2 was also definitely present in the array. 
Chandler has misplaced the list of integers but he wants to impress Monica with his problem solving skills by finding out the minimum and maximum possible sum of all elements of the list of integers.
Can you also help him solve the problem so that he can win over Monica?

-----Input:-----
- First line will contain $T$, the number of testcases. 
- The first line of each test case contains integers $N$, $L$, and $R$. 

-----Output:-----
For each test case print 2 space-separated integers, the minimum and the maximum possible sum of N elements based on the above facts.

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq N \leq 1000$
- $1 \leq L \leq R \leq min(N,20)$

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

4 2 2

5 1 5

-----Sample Output:-----
5 7

5 31

-----EXPLANATION:-----
- 
Example 1: For an array of size 4, with minimum 2 unique integers and maximum 2 unique integers, the possible arrays are (1,1,1,2), (1,1,2,2), (1,2,2,2)
Out of these, the minimum possible sum of elements is 5(1+1+1+2) and maximum possible sum is 7(1+2+2+2)
- 
Example 2: For an array of size 5, with minimum 1 unique integer and maximum 5 unique integers, minimum possible sum of elements is 5(1+1+1+1+1) and maximum possible sum is 31(1+2+4+8+16)
user: Give me Chocolate

Anushka wants to buy chocolates.there are many chocolates in front of her, tagged with their prices.

Anushka has only a certain amount to spend, and she wants to maximize the number of chocolates she buys with this money.

Given a list of prices and an amount to spend, what is the maximum number of chocolates Anushka can buy? 

For example, 

if prices =[1,2,3,4]
and Anushka has k=7 to spend, she can buy items [1,2,3] for 6 , or [3,4] for 7 units of currency. she would choose the first group of 3 items.

Input Format

The first line contains two integers, n and k , the number of priced chocolates and the amount Anushka has to spend.

The next line contains n space-separated integers prices[i]

Constraints

1<= n <= 105

1<= k <= 109

1<= prices[i] <= 109



A chocolate can't be bought multiple times.

Output Format

An integer that denotes the maximum number of chocolates Anushka can buy for her.

Sample Input

7 50

1 12 5 111 200 1000 10

Sample Output

4

Explanation

she can buy only 4 chocolatess at most. These chocolates have the following prices: 1, 12, 5, 10.