vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Vasya often uses public transport. The transport in the city is of two types: trolleys and buses. The city has n buses and m trolleys, the buses are numbered by integers from 1 to n, the trolleys are numbered by integers from 1 to m.

Public transport is not free. There are 4 types of tickets:   A ticket for one ride on some bus or trolley. It costs c_1 burles;  A ticket for an unlimited number of rides on some bus or on some trolley. It costs c_2 burles;  A ticket for an unlimited number of rides on all buses or all trolleys. It costs c_3 burles;  A ticket for an unlimited number of rides on all buses and trolleys. It costs c_4 burles. 

Vasya knows for sure the number of rides he is going to make and the transport he is going to use. He asked you for help to find the minimum sum of burles he will have to spend on the tickets.


-----Input-----

The first line contains four integers c_1, c_2, c_3, c_4 (1 ≤ c_1, c_2, c_3, c_4 ≤ 1000) — the costs of the tickets.

The second line contains two integers n and m (1 ≤ n, m ≤ 1000) — the number of buses and trolleys Vasya is going to use.

The third line contains n integers a_{i} (0 ≤ a_{i} ≤ 1000) — the number of times Vasya is going to use the bus number i.

The fourth line contains m integers b_{i} (0 ≤ b_{i} ≤ 1000) — the number of times Vasya is going to use the trolley number i.


-----Output-----

Print a single number — the minimum sum of burles Vasya will have to spend on the tickets.


-----Examples-----
Input
1 3 7 19
2 3
2 5
4 4 4

Output
12

Input
4 3 2 1
1 3
798
1 2 3

Output
1

Input
100 100 8 100
3 5
7 94 12
100 1 47 0 42

Output
16



-----Note-----

In the first sample the profitable strategy is to buy two tickets of the first type (for the first bus), one ticket of the second type (for the second bus) and one ticket of the third type (for all trolleys). It totals to (2·1) + 3 + 7 = 12 burles.

In the second sample the profitable strategy is to buy one ticket of the fourth type.

In the third sample the profitable strategy is to buy two tickets of the third type: for all buses and for all trolleys.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Soma is a fashionable girl. She absolutely loves shiny stones that she can put on as jewellery accessories. She has been collecting stones since her childhood - now she has become really good with identifying which ones are fake and which ones are not.  Her King requested for her help in mining precious stones, so she has told him which all stones are jewels and which are not. Given her description, your task is  to count the number of jewel stones. 

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

-----Input-----

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


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

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

Output:
3
2
1
0

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You have a tree consisting of n vertices. You want to color each vertex of the tree in one of the k colors such that for any pair of vertices having same color, all the vertices belonging to the path joining them should also have same color. In other words, for any two vertices u, v with same color, all the vertices in the path joining them should also have color same as that of the u (or same as v, as u and v have same color). 

Find out possible number of ways in which you can color the tree satisfying the above property. As the answer could be large, print your answer modulo 109 + 7.

-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
For each test case, first line contains two space separated integers n, k denoting number of vertices in the tree and total number of colors, respectively
Each of the next n - 1 lines contain two space separated integers ui, vi, denoting that there is an edge between vertices ui and vi in the tree.

-----Output-----
For each test case, output a single line corresponding to number of ways of coloring the tree.

-----Constraints-----
- 1 ≤ T ≤ 50
- 1 ≤ n, k ≤ 50
- 1 ≤ ui, vi ≤ n
- ui ≠ vi

-----Example-----
Input
3
3 2
1 2
2 3
3 1
1 2
2 3
4 3
1 2
2 3
2 4

Output:
6
1
39

-----Explanation-----
In the first example, You can color the vertices in the following 6 ways - {1, 1, 1}, {2, 2, 2}, {1, 2, 2}, {1, 1, 2}, {2, 1, 1}, {2, 2, 1}. Note that you can't color the tree in {1, 2, 1} as the vertices in the path connecting vertex 1 and 3, (i.e. 1, 2, 3) don't have same color. You can see that the color of 2nd vertex is not same as that of 1st and 3rd.
In the second example, Only possible coloring you can do is to color all the vertices with color 1.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You have decided to write a book introducing good restaurants.
There are N restaurants that you want to introduce: Restaurant 1, Restaurant 2, ..., Restaurant N. Restaurant i is in city S_i, and your assessment score of that restaurant on a 100-point scale is P_i.
No two restaurants have the same score.
You want to introduce the restaurants in the following order:
 - The restaurants are arranged in lexicographical order of the names of their cities.
 - If there are multiple restaurants in the same city, they are arranged in descending order of score.
Print the identification numbers of the restaurants in the order they are introduced in the book.

-----Constraints-----
 - 1 ≤ N ≤ 100
 - S is a string of length between 1 and 10 (inclusive) consisting of lowercase English letters.
 - 0 ≤ P_i ≤ 100
 - P_i is an integer.
 - P_i ≠ P_j (1 ≤ i < j ≤ N)

-----Input-----
Input is given from Standard Input in the following format:
N
S_1 P_1
:
S_N P_N

-----Output-----
Print N lines. The i-th line (1 ≤ i ≤ N) should contain the identification number of the restaurant that is introduced i-th in the book.

-----Sample Input-----
6
khabarovsk 20
moscow 10
kazan 50
kazan 35
moscow 60
khabarovsk 40

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

The lexicographical order of the names of the three cities is kazan < khabarovsk < moscow. For each of these cities, the restaurants in it are introduced in descending order of score. Thus, the restaurants are introduced in the order 3,4,6,1,5,2.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Mehta woke up after a long sleep, and decided to attend college class which is infact pretty much unusual. But, to somehow survive this boring class,  he asks his friend Verma, to give him a task which he would solve in that boring class. So, Mehta is given the following task.

He has to report the summation of all F(x) for x in range(A,B) where A and B are two given integers that is,

F(x) is defined as sum of powers of primes in prime factorization of x.

For Ex : - F(12) = 3
12 is written as 2^2 * 3^1, so powers are 2 and 1, Hence, F(12) = 2+1 = 3.

So, you being in the same condition as Mehta, decided to solve the same question in the class.

Input:
First Line of the input containts number of test cases T.
Next T lines of input consists of two space separated integers A and B as described in the above task.

Output:
Output the required summation of F(x) for all x in range(A,B) for each test case in a separate line.

Constraints:
A ≤ B
1 ≤ A,B ≤ 10^6
T ≤ 10^6

Note: Large Input/Output Files, use scanf/printf.

SAMPLE INPUT
4
2 4
4 7
2 56
43 2323

SAMPLE OUTPUT
4
6
124
6901

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Enough is enough. Too many times it happened that Vasya forgot to dispose of garbage and his apartment stank afterwards. Now he wants to create a garbage disposal plan and stick to it.

For each of next $n$ days Vasya knows $a_i$ — number of units of garbage he will produce on the $i$-th day. Each unit of garbage must be disposed of either on the day it was produced or on the next day. Vasya disposes of garbage by putting it inside a bag and dropping the bag into a garbage container. Each bag can contain up to $k$ units of garbage. It is allowed to compose and drop multiple bags into a garbage container in a single day.

Being economical, Vasya wants to use as few bags as possible. You are to compute the minimum number of bags Vasya needs to dispose of all of his garbage for the given $n$ days. No garbage should be left after the $n$-th day.


-----Input-----

The first line of the input contains two integers $n$ and $k$ ($1 \le n \le 2\cdot10^5, 1 \le k \le 10^9$) — number of days to consider and bag's capacity. The second line contains $n$ space separated integers $a_i$ ($0 \le a_i \le 10^9$) — the number of units of garbage produced on the $i$-th day.


-----Output-----

Output a single integer — the minimum number of bags Vasya needs to dispose of all garbage. Each unit of garbage should be disposed on the day it was produced or on the next day. No garbage can be left after the $n$-th day. In a day it is allowed to compose and drop multiple bags.


-----Examples-----
Input
3 2
3 2 1

Output
3

Input
5 1
1000000000 1000000000 1000000000 1000000000 1000000000

Output
5000000000

Input
3 2
1 0 1

Output
2

Input
4 4
2 8 4 1

Output
4

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Alf and Beata were two kids who lived long ago, during the time before you could spend Halloween participating in programming competitions. As such, their lives were much more boring than the lives of kids today. How can you survive without programming competitions, you may ask yourself. The answer is easy: you go trick-or-treating!

Every year Alf and Beata went out in their neighbourhood to go trick-or-treating. When they trick-or-treat a house, they get some amount of candy of various sorts. Once the kids have filled up their big bag of candy, they go back home.

Since Alf and Beata are very nice siblings, they want to split all their candy evenly. The siblings have $N$ pieces of candy together. However, they each like every piece a bit differently. Alf hates liquorice, which Beata loves. On the other hand, Alf craves chocolate which Beata finds disgusting. More specifically, Alf assigns the $i$’th piece value $a_ i$ while Beata assigns it value $b_ i$. These values can be negative. They want the absolute difference between the sum of the value of all candy each sibling gets to be as small as possible. Note that each candy must be given to one of the siblings: they can’t throw any candy away.

-----Input-----
The first line of the input contains a single integer $N$ ($1 \le N \le 100$), the number of candies the siblings have collected. The next line contains the $N$ integers $a_1, a_2 \dots , a_ N$ ($-100 \le a_ i \le 100$). The third and final line contains the $N$ integers $b_1, b_2 \dots , b_ N$ ($-100 \le b_ i \le 100$).

-----Output-----
Output a string containing $N$ characters. The $i$’th character should be A if the candy should be given to Alf, and B if it should be given to Beata. If there are multiple solutions, output the lexicographically smallest one.

-----Examples-----
Sample Input:
5
-2 -1 0 1 2
2 1 0 -1 -2
Sample Output:
AAAAA

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given an integer $n$, find each $\boldsymbol{x}$ such that:

$0\leq x\leq n$
$n+x=n\oplus x$

where $\oplus$ denotes the bitwise XOR operator. Return the number of $\boldsymbol{x}$'s satisfying the criteria.

Example 

$n=4$   

There are four values that meet the criteria:  

$4+0=4\oplus0=4$
$4+1=4\oplus1=5$
$4+2=4\oplus2=6$
$4+3=4\oplus3=7$    

Return $4$.  

Function Description

Complete the sumXor function in the editor below.  

sumXor has the following parameter(s): 

- int n: an integer   

Returns 

- int: the number of values found   

Input Format

A single integer, $n$.

Constraints

$0\leq n\leq10^{15}$

Subtasks

$0\leq n\leq100$ for $\textbf{60\%}$ of the maximum score.

Output Format

Sample Input 0

5

Sample Output 0

2

Explanation 0

For $n=5$, the $\boldsymbol{x}$ values $\mbox{0}$ and $2$ satisfy the conditions:

$5+0=5,\:\:5\oplus0=5$
$5+2=7,\:\:5\oplus2=7$

Sample Input 1

10

Sample Output 1

4

Explanation 1

For $n=10$, the $\boldsymbol{x}$ values $\mbox{0}$, $\mbox{1}$, $4$, and $5$ satisfy the conditions:

$10+0=10,~~10\oplus0=10$
$10+1=11,~~10\oplus1=11$
$10+4=14,~~10\oplus4=14$
$10+5=15,~~10\oplus5=15$

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Reading books is one of Sasha's passions. Once while he was reading one book, he became acquainted with an unusual character. The character told about himself like that: "Many are my names in many countries. Mithrandir among the Elves, Tharkûn to the Dwarves, Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not."

And at that moment Sasha thought, how would that character be called in the East? In the East all names are palindromes. A string is a palindrome if it reads the same backward as forward. For example, such strings as "kazak", "oo" and "r" are palindromes, but strings "abb" and "ij" are not. 

Sasha believed that the hero would be named after one of the gods of the East. As long as there couldn't be two equal names, so in the East people did the following: they wrote the original name as a string on a piece of paper, then cut the paper minimum number of times $k$, so they got $k+1$ pieces of paper with substrings of the initial string, and then unite those pieces together to get a new string. Pieces couldn't be turned over, they could be shuffled.

In this way, it's possible to achive a string abcdefg from the string f|de|abc|g using $3$ cuts (by swapping papers with substrings f and abc). The string cbadefg can't be received using the same cuts.

More formally, Sasha wants for the given palindrome $s$ find such minimum $k$, that you can cut this string into $k + 1$ parts, and then unite them in such a way that the final string will be a palindrome and it won't be equal to the initial string $s$. It there is no answer, then print "Impossible" (without quotes).


-----Input-----

The first line contains one string $s$ ($1 \le |s| \le 5\,000$) — the initial name, which consists only of lowercase Latin letters. It is guaranteed that $s$ is a palindrome.


-----Output-----

Print one integer $k$ — the minimum number of cuts needed to get a new name, or "Impossible" (without quotes).


-----Examples-----
Input
nolon

Output
2

Input
otto

Output
1

Input
qqqq

Output
Impossible

Input
kinnikkinnik

Output
1



-----Note-----

In the first example, you can cut the string in those positions: no|l|on, and then unite them as follows on|l|no. It can be shown that there is no solution with one cut.

In the second example, you can cut the string right in the middle, and swap peaces, so you get toot.

In the third example, you can't make a string, that won't be equal to the initial one.

In the fourth example, you can cut the suffix nik and add it to the beginning, so you get nikkinnikkin.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Game is played on the field of the size 1 x N cells. The cells are numbered from 1 to N. In the i-th cell there are 2 positive integers - Ai and Bi.

Initially, the player stands at the fictive cell with the index 0 that is located right before all the N cells of the board. Then, he makes moves. Each move consists in moving by no more than by K cells forward. The goal of the game is to reach the fictive N+1-th cell that is located right after all the N cells.

After the N+1-th cell is reached, the player's penalty is calculated. The penalty equals to max(Ax) * max(By), where x and y are the indices of the cells that were visited in between (during the movement to the N+1-th cell).

Please find the minimal possible penalty that can be reached in this game.

INPUT
The first line of input contains two single space separated integer numbers - N and K respectively.
Then, there are N lines, each containing a pair of single space separated integers - Ai and Bi respectively.

OUTPUT

Output the minimal possible penalty on the first line.

CONSTRAINTS
1 ≤ K ≤ N
1 ≤ N ≤ 1000, 1 ≤ Ai, Bi ≤ 32000

SAMPLE INPUT
4 3
4 8
5 9
12 23
1 6

SAMPLE OUTPUT
32

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Takahashi has N blue cards and M red cards.
A string is written on each card. The string written on the i-th blue card is s_i, and the string written on the i-th red card is t_i.
Takahashi will now announce a string, and then check every card. Each time he finds a blue card with the string announced by him, he will earn 1 yen (the currency of Japan); each time he finds a red card with that string, he will lose 1 yen.
Here, we only consider the case where the string announced by Takahashi and the string on the card are exactly the same. For example, if he announces atcoder, he will not earn money even if there are blue cards with atcoderr, atcode, btcoder, and so on. (On the other hand, he will not lose money even if there are red cards with such strings, either.)
At most how much can he earn on balance?
Note that the same string may be written on multiple cards.

-----Constraints-----
 - N and M are integers.
 - 1 \leq N, M \leq 100
 - s_1, s_2, ..., s_N, t_1, t_2, ..., t_M are all strings of lengths between 1 and 10 (inclusive) consisting of lowercase English letters.

-----Input-----
Input is given from Standard Input in the following format:
N
s_1
s_2
:
s_N
M
t_1
t_2
:
t_M

-----Output-----
If Takahashi can earn at most X yen on balance, print X.

-----Sample Input-----
3
apple
orange
apple
1
grape

-----Sample Output-----
2

He can earn 2 yen by announcing apple.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You're given a string $\mbox{S}$ of $N$ characters. It's known that the string consists of lowercase Latin letters. The string is generated randomly. That means that every symbol is chosen randomly and independently from others from the set {'a', 'b', ..., 'z'}. All the letters have equal probability to appear.

You're given $\mbox{Q}$ queries on this string. Each query is of the form P C, where $\mbox{P}$ is an integer between $1$ and $N$ (both inclusive) and $\mbox{C}$ is a character from the set {'a', 'b', ..., 'z'}. Both $\mbox{P}$ and $\mbox{C}$ were chosen at random and independently from other queries. 

When you have a query of the form P C you have to change the  $P^{th}$ symbol of $\mbox{S}$ to $\mbox{C}$. After every change we ask you to output the number of distinct nonempty sub-strings of $\mbox{S}$.

Input Format

The first line of input consists of two single space-separated integers $N$ and $\mbox{Q}$, the length of the string $\mbox{S}$ and the number of queries, respectively.

The second line contains string $\mbox{S}$.

The following $\mbox{Q}$ lines describe the queries in the form P C, where $\mbox{P}$ and $\mbox{C}$ are also separated with a single space.

Constraints 

$4\leq N\leq75000$ 

$4\leq Q\leq75000$ 

Output Format

Output $\mbox{Q}$ lines. Output the number of distinct substrings of $\mbox{S}$ after the $i^{th}$ query on the $i^{th}$  line of the output.

Sample Input
4 4 
aaab
1 a
2 b
3 c
4 d

Sample Output
7
7
9
10

Explanation

After replacing the character at the first index with a, we still have the original string aaab. The total non empty substrings of aaab are 

a b aa ab aaa aab aaab

hence 7. 

After replacing the character at the second index with b, we have the string abab. The non-empty substrings of abab are 

a b ab ba aba bab abab

hence 7. 

After replacing the character at the third index with c, we have the string abcb. The total non empty substrings of abcb are

a b c ab bc cb abc bcb abcb

hence 9.   

After replacing the character at the fourth index with d, we have the string abcd. The total non empty substrings of abcd are 

a b c d ab bc cd abc bcd abcd

hence 10. 

Scoring

There are 12 test cases.  

The first four test cases N = 100 and Q = 500 

The next four test cases N = 75000 and Q = 10 

The last four test cases N = 75000 and Q = 75000

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of $n$ non-negative integers.

If there are exactly $K$ distinct values in the array, then we need $k = \lceil \log_{2} K \rceil$ bits to store each value. It then takes $nk$ bits to store the whole file.

To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers $l \le r$, and after that all intensity values are changed in the following way: if the intensity value is within the range $[l;r]$, we don't change it. If it is less than $l$, we change it to $l$; if it is greater than $r$, we change it to $r$. You can see that we lose some low and some high intensities.

Your task is to apply this compression in such a way that the file fits onto a disk of size $I$ bytes, and the number of changed elements in the array is minimal possible.

We remind you that $1$ byte contains $8$ bits.

$k = \lceil log_{2} K \rceil$ is the smallest integer such that $K \le 2^{k}$. In particular, if $K = 1$, then $k = 0$.


-----Input-----

The first line contains two integers $n$ and $I$ ($1 \le n \le 4 \cdot 10^{5}$, $1 \le I \le 10^{8}$) — the length of the array and the size of the disk in bytes, respectively.

The next line contains $n$ integers $a_{i}$ ($0 \le a_{i} \le 10^{9}$) — the array denoting the sound file.


-----Output-----

Print a single integer — the minimal possible number of changed elements.


-----Examples-----
Input
6 1
2 1 2 3 4 3

Output
2

Input
6 2
2 1 2 3 4 3

Output
0

Input
6 1
1 1 2 2 3 3

Output
2



-----Note-----

In the first example we can choose $l=2, r=3$. The array becomes 2 2 2 3 3 3, the number of distinct elements is $K=2$, and the sound file fits onto the disk. Only two values are changed.

In the second example the disk is larger, so the initial file fits it and no changes are required.

In the third example we have to change both 1s or both 3s.

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