vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Problem Statement 
Unseen gang is the team of most wanted criminal. Unseen gang has planted bombs in different street and corner of the city. Gang members are sitting in the other part of the city, far away from the bomb site. They are controlling the bomb by sending the activation signal in the form of encrypted code.The Enigma crew has found the solution for the encrypted code. They came to know that the code is in the form of string S. Dividing the string up to its length L into many substrings of length N will give them the location of the bomb site.

Your job is to help the Enigma crew in finding the decrypted code. So, they can track the bomb site.

Input Format
The first line contain a string S.
In the second line integer N the length of the substring is given.

Output Format
Output line contain the total number of substrings each in new line.

Constraints 
1 ≤ L ≤ 10000
1 ≤ N=20

SAMPLE INPUT
Vhaveplanted bomb @allthe location intheCITY.
8

SAMPLE OUTPUT
Vhavepla
nted bom
b @allth
e locati
on inthe
CITY.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
There are N towns located in a line, conveniently numbered 1 through N. Takahashi the merchant is going on a travel from town 1 to town N, buying and selling apples.
Takahashi will begin the travel at town 1, with no apple in his possession. The actions that can be performed during the travel are as follows:
 - Move: When at town i (i < N), move to town i + 1.
 - Merchandise: Buy or sell an arbitrary number of apples at the current town. Here, it is assumed that one apple can always be bought and sold for A_i yen (the currency of Japan) at town i (1 ≦ i ≦ N), where A_i are distinct integers. Also, you can assume that he has an infinite supply of money.
For some reason, there is a constraint on merchandising apple during the travel: the sum of the number of apples bought and the number of apples sold during the whole travel, must be at most T. (Note that a single apple can be counted in both.)
During the travel, Takahashi will perform actions so that the profit of the travel is maximized. Here, the profit of the travel is the amount of money that is gained by selling apples, minus the amount of money that is spent on buying apples. Note that we are not interested in apples in his possession at the end of the travel.
Aoki, a business rival of Takahashi, wants to trouble Takahashi by manipulating the market price of apples. Prior to the beginning of Takahashi's travel, Aoki can change A_i into another arbitrary non-negative integer A_i' for any town i, any number of times. The cost of performing this operation is |A_i - A_i'|. After performing this operation, different towns may have equal values of A_i.
Aoki's objective is to decrease Takahashi's expected profit by at least 1 yen. Find the minimum total cost to achieve it. You may assume that Takahashi's expected profit is initially at least 1 yen.

-----Constraints-----
 - 1 ≦ N ≦ 10^5
 - 1 ≦ A_i ≦ 10^9 (1 ≦ i ≦ N)
 - A_i are distinct.
 - 2 ≦ T ≦ 10^9
 - In the initial state, Takahashi's expected profit is at least 1 yen.

-----Input-----
The input is given from Standard Input in the following format:
N T
A_1 A_2 ... A_N

-----Output-----
Print the minimum total cost to decrease Takahashi's expected profit by at least 1 yen.

-----Sample Input-----
3 2
100 50 200

-----Sample Output-----
1

In the initial state, Takahashi can achieve the maximum profit of 150 yen as follows:
 - Move from town 1 to town 2.
 - Buy one apple for 50 yen at town 2.
 - Move from town 2 to town 3.
 - Sell one apple for 200 yen at town 3.
If, for example, Aoki changes the price of an apple at town 2 from 50 yen to 51 yen, Takahashi will not be able to achieve the profit of 150 yen. The cost of performing this operation is 1, thus the answer is 1.
There are other ways to decrease Takahashi's expected profit, such as changing the price of an apple at town 3 from 200 yen to 199 yen.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Purple rain falls in the magic kingdom of Linearland which is a straight, thin peninsula. 

On close observation however, Prof. Nelson Rogers finds that actually it is a mix of Red and Blue drops.

In his zeal, he records the location and color of the raindrops in different locations along the peninsula. Looking at the data, Professor Rogers wants to know which part of Linearland had the “least” purple rain.

After some thought, he decides to model this problem as follows. Divide the peninsula into $n$ sections and number them West to East from $1$ to $n$. Then, describe the raindrops as a sequence of R and B, depending on whether the rainfall in each section is primarily red or blue. Finally, find a subsequence of where the difference between the number of R and the number of B is maximized.

-----Input-----
The input consists of a single line containing a string of $n$ characters ($1 \le n \le 10^5$), describing the color of the raindrops in sections $1$ to $n$.

It is guaranteed that the string consists of uppercase ASCII letters ‘R’ and ‘B’ only.

-----Output-----
Print, on a single line, two space-separated integers that describe the starting and ending positions of the part of Linearland that had the least purple rain.

If there are multiple possible answers, print the one that has the Westernmost (smallest-numbered) starting section. If there are multiple answers with the same Westernmost starting section, print the one with the Westernmost ending section.

-----Examples-----
Sample Input:
BBRRBRRBRB
Sample Output:
3 7

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Buses Between Cities

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Buses run between the cities *A* and *B*, the first one is at 05:00 AM and the last one departs not later than at 11:59 PM. A bus from the city *A* departs every *a* minutes and arrives to the city *B* in a *t**a* minutes, and a bus from the city *B* departs every *b* minutes and arrives to the city *A* in a *t**b* minutes.

The driver Simion wants to make his job diverse, so he counts the buses going towards him. Simion doesn't count the buses he meet at the start and finish.

You know the time when Simion departed from the city *A* to the city *B*. Calculate the number of buses Simion will meet to be sure in his counting.

Input Specification:
The first line contains two integers *a*,<=*t**a* (1<=≤<=*a*,<=*t**a*<=≤<=120) — the frequency of the buses from the city *A* to the city *B* and the travel time. Both values are given in minutes.

The second line contains two integers *b*,<=*t**b* (1<=≤<=*b*,<=*t**b*<=≤<=120) — the frequency of the buses from the city *B* to the city *A* and the travel time. Both values are given in minutes.

The last line contains the departure time of Simion from the city *A* in the format hh:mm. It is guaranteed that there are a bus from the city *A* at that time. Note that the hours and the minutes are given with exactly two digits.

Output Specification:
Print the only integer *z* — the number of buses Simion will meet on the way. Note that you should not count the encounters in cities *A* and *B*.

Demo Input:
['10 30\n10 35\n05:20\n', '60 120\n24 100\n13:00\n']

Demo Output:
['5\n', '9\n']

Note:
In the first example Simion departs form the city *A* at 05:20 AM and arrives to the city *B* at 05:50 AM. He will meet the first 5 buses from the city *B* that departed in the period [05:00 AM - 05:40 AM]. Also Simion will meet a bus in the city *B* at 05:50 AM, but he will not count it.

Also note that the first encounter will be between 05:26 AM and 05:27 AM (if we suggest that the buses are go with the sustained speed).

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
BooBoo is a smart baby who likes to travel around cities. And he is on a trip to Europe right now! Smart that he is, he has made a list of N cities to visit, and for each city he has M popular places to visit in each city. But being a baby, he does get exhausted pretty quickly and thus plans his trip in an all together different way. For a trip to be successful and non exhausting, BooBoo decides that he will visit exactly one city everyday and in each city, he will visit only one of the M popular places. He has also decided that it's optimal to move across the cities in order 1,2,...,N.

Now there's one more constraint related to travelling : Cost! Since Europe trips are pretty much popular, there are special travelling schemes in offer for the travelers. Let's assume you are currently at the j^{th} place in city i and you plan to move to k^{th} place of the next city. This move is only possible if and only if the lowest prime factor of both j and k is same. The cost for any such valid move is equal to A_{ij} if j=k, otherwise the cost is equal to B_{ij}. 1 is treated as an exception : we assume that all j can lead to k if k = 1. For the first city, you can visit any place you wish to start with without any restriction.

BooBoo has other trips lined up and hence would like you to help him minimize the cost of his successful and non exhausting Europe trip. Can you help him out?

Input Format

The first line contains two space separated integers N and M. The next line contains S_0,P,Q and R, which are inputs to the generator for matrix A. The next line contains W_0,X,Y and Z, which are inputs to the generator for matrix B.

Generator

for(int i = 0; i < (N*M); i++){
    S[i + 1] = (P * S[i] * S[i] + Q * S[i] + R) mod 1000000003
    A[(i/M) + 1][(i%M) + 1] = S[i + 1]
}

for(int i = 0; i < (N*M); i++){
        W[i + 1] = (X * W[i] * W[i] + Y * W[i] + Z) mod 1000000003
        B[(i/M) + 1][(i%M) + 1] = W[i + 1]
    }

Output Format

Output only one integer, the minimum cost of travelling across all N cities.

Constraints

1 ≤ N ≤ 2000
1 ≤ M ≤ 10000
0 ≤ P,Q,R,S_0 ≤ 10^9
0 ≤ X,Y,Z,W_0 ≤ 10^9

SAMPLE INPUT
3 3
2 0 1 0
1 0 2 0

SAMPLE OUTPUT
4

Explanation

The matrix A generated is : 

2 2 2
2 2 2
2 2 2

The matrix B generated is :

2 4 8
16 32 64
128 256 512

One of the possible ways is to visit place 1 in all 3 cities.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Venkatesh wants to gift his girlfriend with chocolates (he is very cheap, so he buys Gems). He has purchased n boxes, where the i-th box contains fi chocolates. All chocolates in a single box are of the same color (hence they are indistinguishable). Also, no two boxes have chocolates of the same color.

Now Venkatesh wants to select exactly s chocolates from the boxes to gift his girlfriend. Venkatesh would like to know, in how many different ways can he select the chocolates from each box? (He can obviously code it in seconds, but he wants you do it for him) Since this number may be very large, he asks you to find the number modulo (10^9+7).

Venkatesh considers two ways(cases) different if there is at least one box from which different number of chocolates are selected in these two ways.

Input
The first line of input contains two space-separated integers n and s (n in 1 to 20, s in 0 to 10^14).

The second line contains n space-separated integers f1,f2,... fn (fi in 0 to 10^12).

Output
Output a single integer — the number of ways in which Venkatesh can select the chocolates modulo (10^9+7).

Sample test(s)
Input
2 3
1 3
Output
2
Input
2 4
2 2
Output
1
Input
3 5
1 3 2
Output
3

Sample 1. There are two ways of selecting 3 chocolates: {1,2} and {0,3}. 
Sample 2. There is only one way of selecting 4 chocolates: {2,2}. 
Sample 3. There are three ways of selecting 5 chocolates: {1,2,2}, {0,3,2}, and {1,3,1}. 

SAMPLE INPUT
2 3
1 3

SAMPLE OUTPUT
2

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Andy got a box of candies for Christmas. In fact, he discovered that the box contained several identical smaller boxes, and they could contain even smaller boxes, and so on. Formally, we say that candies are boxes of level 0, and for 1 ≤ i ≤ n, a level i box contains ai boxes of level i - 1. The largest box has level n. Andy realized that it can take quite a long time to open all the boxes before he actually gets to eat some candies, so he put the box aside in frustration.

But today being his birthday, some friends came to visit Andy, and Andy decided to share some candies with them. In order to do that, he must open some of the boxes. Naturally, Andy can not open a box that is still inside an unopened box. If Andy wants to retrieve X candies, what is the least number of boxes he must open? You must help him answer many such queries. Each query is independent.

-----Input-----
- The first line contains two integers n and m, which refer to the level of the largest box, and the number of queries respectively.
- The second line contains n integers a1, ..., an.
- The third line contains m integers X1, ..., Xm.

-----Output-----
- Print m integers each in a new line, ith of them equal to the smallest number of boxes Andy must open in order to retrieve at least Xi candies.

-----Constraints-----
- 1 ≤ n,m ≤ 300000
- 1 ≤ ai ≤ 109
- 1 ≤ Xi ≤ 1012
- It is guaranteed that the total number of candies is at least Xi for all i

-----Example-----
Input 1:
5 1
1 1 1 1 1
1

Output 1:
5

Input 2:
3 3
3 3 3
2 8 13

Output 2:
3
5
8

-----Explanation-----
Testcase 1: The only candy is contained in five levels of boxes. 
Testcase 2: In the third query, for 13 candies, Andy should open the largest box, two level-2 boxes, and finally five of six available level-1 boxes. Each of those boxes will contain 3 level-0 boxes (which are candies). So he'll have 15 candies in total, but he needs only 13 of them.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Lotte is competing in a programming contest. Her team has already solved $k$ out of the $n$ problems in the problem set, but as the problems become harder, she begins to lose focus and her mind starts to wander. 

She recalls hearing the judges talk about the difficulty of the problems, which they rate on an integer scale from $0$ to $100$, inclusive. In fact, one of the judges said that “the problem set has never been so tough, the average difficulty of the problems in the problem set is $d$!”

She starts thinking about the problems her team has solved so far, and comes up with an estimate $s$ for their average difficulty. In hope of gaining some motivation, Lotte wonders if she can use this information to determine the average difficulty of the remaining problems.

-----Input-----
The input consists of:
 - One line with two integers $n$ and $k$ ($2\leq n\leq 10^6$, $0 < k < n$), the total number of problems and the number of problems Lotte’s team has solved so far.
 - One line with two integers $d$ and $s$ ($0\leq d,s \leq 100$), the average difficulty of all the problems and Lotte’s estimate of the average difficulty of the problems her team has solved.

-----Output-----
Assuming Lotte’s estimate is correct, output the average difficulty of the unsolved problems, or “impossible” if the average difficulty does not exist. Your answer should have an absolute or relative error of at most $10^{-6}$.

-----Examples-----
Sample Input 1:
2 1
70 50
Sample Output 1:
90.00

Sample Input 2:
10 3
80 90
Sample Output 2:
75.7142857

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Little Elephant and Cards

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
The Little Elephant loves to play with color cards.

He has *n* cards, each has exactly two colors (the color of the front side and the color of the back side). Initially, all the cards lay on the table with the front side up. In one move the Little Elephant can turn any card to the other side. The Little Elephant thinks that a set of cards on the table is funny if at least half of the cards have the same color (for each card the color of the upper side is considered).

Help the Little Elephant to find the minimum number of moves needed to make the set of *n* cards funny.

Input Specification:
The first line contains a single integer *n* (1<=≤<=*n*<=≤<=105) — the number of the cards. The following *n* lines contain the description of all cards, one card per line. The cards are described by a pair of positive integers not exceeding 109 — colors of both sides. The first number in a line is the color of the front of the card, the second one — of the back. The color of the front of the card may coincide with the color of the back of the card.

The numbers in the lines are separated by single spaces.

Output Specification:
On a single line print a single integer — the sought minimum number of moves. If it is impossible to make the set funny, print -1.

Demo Input:
['3\n4 7\n4 7\n7 4\n', '5\n4 7\n7 4\n2 11\n9 7\n1 1\n']

Demo Output:
['0\n', '2\n']

Note:
In the first sample there initially are three cards lying with colors 4, 4, 7. Since two of the three cards are of the same color 4, you do not need to change anything, so the answer is 0.

In the second sample, you can turn the first and the fourth cards. After that three of the five cards will be of color 7.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Ayrat has number n, represented as it's prime factorization p_{i} of size m, i.e. n = p_1·p_2·...·p_{m}. Ayrat got secret information that that the product of all divisors of n taken modulo 10^9 + 7 is the password to the secret data base. Now he wants to calculate this value.


-----Input-----

The first line of the input contains a single integer m (1 ≤ m ≤ 200 000) — the number of primes in factorization of n. 

The second line contains m primes numbers p_{i} (2 ≤ p_{i} ≤ 200 000).


-----Output-----

Print one integer — the product of all divisors of n modulo 10^9 + 7.


-----Examples-----
Input
2
2 3

Output
36

Input
3
2 3 2

Output
1728



-----Note-----

In the first sample n = 2·3 = 6. The divisors of 6 are 1, 2, 3 and 6, their product is equal to 1·2·3·6 = 36.

In the second sample 2·3·2 = 12. The divisors of 12 are 1, 2, 3, 4, 6 and 12. 1·2·3·4·6·12 = 1728.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given several queries. In the i-th query you are given a single positive integer n_{i}. You are to represent n_{i} as a sum of maximum possible number of composite summands and print this maximum number, or print -1, if there are no such splittings.

An integer greater than 1 is composite, if it is not prime, i.e. if it has positive divisors not equal to 1 and the integer itself.


-----Input-----

The first line contains single integer q (1 ≤ q ≤ 10^5) — the number of queries.

q lines follow. The (i + 1)-th line contains single integer n_{i} (1 ≤ n_{i} ≤ 10^9) — the i-th query.


-----Output-----

For each query print the maximum possible number of summands in a valid splitting to composite summands, or -1, if there are no such splittings.


-----Examples-----
Input
1
12

Output
3

Input
2
6
8

Output
1
2

Input
3
1
2
3

Output
-1
-1
-1



-----Note-----

12 = 4 + 4 + 4 = 4 + 8 = 6 + 6 = 12, but the first splitting has the maximum possible number of summands.

8 = 4 + 4, 6 can't be split into several composite summands.

1, 2, 3 are less than any composite number, so they do not have valid splittings.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
In a galaxy far, far away Lesha the student has just got to know that he has an exam in two days. As always, he hasn't attended any single class during the previous year, so he decided to spend the remaining time wisely.

Lesha knows that today he can study for at most a hours, and he will have b hours to study tomorrow. Note that it is possible that on his planet there are more hours in a day than on Earth. Lesha knows that the quality of his knowledge will only depend on the number of lecture notes he will read. He has access to an infinite number of notes that are enumerated with positive integers, but he knows that he can read the first note in one hour, the second note in two hours and so on. In other words, Lesha can read the note with number k in k hours. Lesha can read the notes in arbitrary order, however, he can't start reading a note in the first day and finish its reading in the second day.

Thus, the student has to fully read several lecture notes today, spending at most a hours in total, and fully read several lecture notes tomorrow, spending at most b hours in total. What is the maximum number of notes Lesha can read in the remaining time? Which notes should he read in the first day, and which — in the second?

Input

The only line of input contains two integers a and b (0 ≤ a, b ≤ 10^{9}) — the number of hours Lesha has today and the number of hours Lesha has tomorrow.

Output

In the first line print a single integer n (0 ≤ n ≤ a) — the number of lecture notes Lesha has to read in the first day. In the second line print n distinct integers p_1, p_2, …, p_n (1 ≤ p_i ≤ a), the sum of all p_i should not exceed a.

In the third line print a single integer m (0 ≤ m ≤ b) — the number of lecture notes Lesha has to read in the second day. In the fourth line print m distinct integers q_1, q_2, …, q_m (1 ≤ q_i ≤ b), the sum of all q_i should not exceed b.

All integers p_i and q_i should be distinct. The sum n + m should be largest possible.

Examples

Input

3 3


Output

1
3 
2
2 1 

Input

9 12


Output

2
3 6
4
1 2 4 5

Note

In the first example Lesha can read the third note in 3 hours in the first day, and the first and the second notes in one and two hours correspondingly in the second day, spending 3 hours as well. Note that Lesha can make it the other way round, reading the first and the second notes in the first day and the third note in the second day.

In the second example Lesha should read the third and the sixth notes in the first day, spending 9 hours in total. In the second day Lesha should read the first, second fourth and fifth notes, spending 12 hours in total.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Read problems statements in Mandarin Chinese  and Russian. 

Run has given you a list of statements of the form "A+B=C", where A, B and C consist only of decimal digits and small latin letters from 'a' to 'f'. Moreover, the first symbol of A, B, C is always not a zero and the length of A, B, C is not greater than 8.  How many statements have an integer Q in the range [2; 16] such that A+B equals to C in the base Q?

------ Input ------ 

The first line of input consists of an integer T - the number of statements. Then, T statements in the form "A+B=C" (without any spaces) follow, each on a separate line.

------ Output ------ 

Output an answer to the problem of the first line of output.

------ Scoring ------ 

T = 10^{5}, Every statement is either true in the base 10, either false in all the bases : 50 points.
T = 10^{5}, No additional constraints : 50 points. 

----- Sample Input 1 ------ 
3
2+2=10
1+2=a
3+5=8
----- Sample Output 1 ------ 
2

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
##Task:

You have to write a function **pattern** which creates the following pattern upto n number of rows. *If the Argument is 0 or a Negative Integer then it should return "" i.e. empty string.*
   
##Examples:

pattern(4):

    1234
    234
    34
    4
    
pattern(6):
 
    123456
    23456
    3456
    456
    56
    6



```Note: There are no blank spaces```

```Hint: Use \n in string to jump to next line```

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.