apaz/codeforces-genesys huggingface dataset:
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?

## Input Format
The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.

## Output Format
Print a single integer — the minimum sum in rubles that Ann will need to spend.

## Examples
```input
6 2 1 2
```
```output
6
```
-----
```input
5 2 2 3
```
```output
8
```

## Note
In the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
The start of the new academic year brought about the problem of accommodation students into dormitories. One of such dormitories has a a × b square meter wonder room. The caretaker wants to accommodate exactly n students there. But the law says that there must be at least 6 square meters per student in a room (that is, the room for n students must have the area of at least 6n square meters). The caretaker can enlarge any (possibly both) side of the room by an arbitrary positive integer of meters. Help him change the room so as all n students could live in it and the total area of the room was as small as possible.

## Input Format
The first line contains three space-separated integers n, a and b (1 ≤ n, a, b ≤ 109) — the number of students and the sizes of the room.

## Output Format
Print three integers s, a1 and b1 (a ≤ a1; b ≤ b1) — the final area of the room and its sizes. If there are multiple optimal solutions, print any of them.

## Examples
```input
3 3 5
```
```output
18
3 6
```
-----
```input
2 4 4
```
```output
16
4 4
```

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
You've got array a[1], a[2], ..., a[n], consisting of n integers. Count the number of ways to split all the elements of the array into three contiguous parts so that the sum of elements in each part is the same.

More formally, you need to find the number of such pairs of indices i, j (2 ≤ i ≤ j ≤ n - 1), that $$\sum_{k=1}^{i-1}a_k=\sum_{k=i}^ja_k=\sum_{k=j+1}^na_k$$.

## Input Format
The first line contains integer n (1 ≤ n ≤ 5·105), showing how many numbers are in the array. The second line contains n integers a[1], a[2], ..., a[n] (|a[i]| ≤  109) — the elements of array a.

## Output Format
Print a single integer — the number of ways to split the array into three parts with the same sum.

## Examples
```input
5
1 2 3 0 3
```
```output
2
```
-----
```input
4
0 1 -1 0
```
```output
1
```
-----
```input
2
4 1
```
```output
0
```

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
Peter has a sequence of integers a1, a2, ..., an. Peter wants all numbers in the sequence to equal h. He can perform the operation of "adding one on the segment [l, r]": add one to all elements of the sequence with indices from l to r (inclusive). At that, Peter never chooses any element as the beginning of the segment twice. Similarly, Peter never chooses any element as the end of the segment twice. In other words, for any two segments [l1, r1] and [l2, r2], where Peter added one, the following inequalities hold: l1 ≠ l2 and r1 ≠ r2.

How many distinct ways are there to make all numbers in the sequence equal h? Print this number of ways modulo 1000000007 (109 + 7). Two ways are considered distinct if one of them has a segment that isn't in the other way.

## Input Format
The first line contains two integers n, h (1 ≤ n, h ≤ 2000). The next line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 2000).

## Output Format
Print a single integer — the answer to the problem modulo 1000000007 (109 + 7).

## Examples
```input
3 2
1 1 1
```
```output
4
```
-----
```input
5 1
1 1 1 1 1
```
```output
1
```
-----
```input
4 3
3 2 1 1
```
```output
0
```

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one.

Your friend often comes up with different statements. He has recently supposed that if the pair (a, b) is coprime and the pair (b, c) is coprime, then the pair (a, c) is coprime.

You want to find a counterexample for your friend's statement. Therefore, your task is to find three distinct numbers (a, b, c), for which the statement is false, and the numbers meet the condition l ≤ a < b < c ≤ r.

More specifically, you need to find three numbers (a, b, c), such that l ≤ a < b < c ≤ r, pairs (a, b) and (b, c) are coprime, and pair (a, c) is not coprime.

## Input Format
The single line contains two positive space-separated integers l, r (1 ≤ l ≤ r ≤ 1018; r - l ≤ 50).

## Output Format
Print three positive space-separated integers a, b, c — three distinct numbers (a, b, c) that form the counterexample. If there are several solutions, you are allowed to print any of them. The numbers must be printed in ascending order.

If the counterexample does not exist, print the single number -1.

## Examples
```input
2 4
```
```output
2 3 4
```
-----
```input
10 11
```
```output
-1
```
-----
```input
900000000000000009 900000000000000029
```
```output
900000000000000009 900000000000000010 900000000000000021
```

## Note
In the first sample pair (2, 4) is not coprime and pairs (2, 3) and (3, 4) are.

In the second sample you cannot form a group of three distinct integers, so the answer is -1.

In the third sample it is easy to see that numbers 900000000000000009 and 900000000000000021 are divisible by three.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
You have two friends. You want to present each of them several positive integers. You want to present cnt1 numbers to the first friend and cnt2 numbers to the second friend. Moreover, you want all presented numbers to be distinct, that also means that no number should be presented to both friends.

In addition, the first friend does not like the numbers that are divisible without remainder by prime number x. The second one does not like the numbers that are divisible without remainder by prime number y. Of course, you're not going to present your friends numbers they don't like.

Your task is to find such minimum number v, that you can form presents using numbers from a set 1, 2, ..., v. Of course you may choose not to present some numbers at all.

A positive integer number greater than 1 is called prime if it has no positive divisors other than 1 and itself.

## Input Format
The only line contains four positive integers cnt1, cnt2, x, y (1 ≤ cnt1, cnt2 < 109; cnt1 + cnt2 ≤ 109; 2 ≤ x < y ≤ 3·104) — the numbers that are described in the statement. It is guaranteed that numbers x, y are prime.

## Output Format
Print a single integer — the answer to the problem.

## Examples
```input
3 1 2 3
```
```output
5
```
-----
```input
1 3 2 3
```
```output
4
```

## Note
In the first sample you give the set of numbers {1, 3, 5} to the first friend and the set of numbers {2} to the second friend. Note that if you give set {1, 3, 5} to the first friend, then we cannot give any of the numbers 1, 3, 5 to the second friend.

In the second sample you give the set of numbers {3} to the first friend, and the set of numbers {1, 2, 4} to the second friend. Thus, the answer to the problem is 4.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
На плоскости расположены два многоугольника A и B. Многоугольник A вращается вокруг точки P, а многоугольник B — вокруг точки Q. Каждый многоугольник вращается с постоянной угловой скоростью по часовой стрелке вокруг своей точки, угловые скорости вращения многоугольников совпадают.

Требуется определить, произойдет ли когда-нибудь столкновение между многоугольниками. Под столкновением подразумевается ситуация, в которой многоугольники имеют хотя бы одну общую точку.

Гарантируется, что в момент времени 0 многоугольники A и B не пересекаются, и ни один из многоугольников не содержится целиком внутри другого.

Обратите внимание, что:

- многоугольники могут не являться выпуклыми;
- точки P и Q могут находиться на границе или вне своих многоугольников.

## Input Format
В первой строке через пробел записаны координаты точки P.

Во второй строке записано одно целое число n (3 ≤ n ≤ 1000) — количество вершин многоугольника A.

В каждой их следующих n строк записано по два числа, разделенных пробелом — координаты очередной вершины многоугольника A.

Следующая строка оставлена пустой.

Далее следуют через пробел координаты точки Q.

В следующей строке находится одно целое число m (3 ≤ m ≤ 1000) — количество вершин многоугольника B. Далее в m строках в аналогичном формате описаны координаты координаты вершин многоугольника B.

Вершины обоих многоугольников перечислены в порядке обхода против часовой стрелки. Все координаты точек — целые числа, по модулю не превосходящие 104.

## Output Format
Выведите «YES», если столкновение произойдет, и «NO» в противном случае.

## Examples
```input
1 0
4
0 0
1 0
1 5
0 5
9 0
4
9 0
9 -5
10 -5
10 0
```
```output
YES
```
-----
```input
0 0
3
1 0
2 -1
2 1
0 0
3
-1 0
-2 1
-2 -1
```
```output
NO
```

## Note
Многоугольником называется замкнутая ломаная без самопересечений и самокасаний.

Картинка к первому примеру:

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
Assume that sk(n) equals the sum of digits of number n in the k-based notation. For example, s2(5) = s2(1012) = 1 + 0 + 1 = 2, s3(14) = s3(1123) = 1 + 1 + 2 = 4.

The sequence of integers a0, ..., an - 1 is defined as $$a_{j}=s_{k}(j)\bmod k$$. Your task is to calculate the number of distinct subsequences of sequence a0, ..., an - 1. Calculate the answer modulo 109 + 7.

Sequence a1, ..., ak is called to be a subsequence of sequence b1, ..., bl, if there is a sequence of indices 1 ≤ i1 < ... < ik ≤ l, such that a1 = bi1, ..., ak = bik. In particular, an empty sequence (i.e. the sequence consisting of zero elements) is a subsequence of any sequence.

## Input Format
The first line contains two space-separated numbers n and k (1 ≤ n ≤ 1018, 2 ≤ k ≤ 30).

## Output Format
In a single line print the answer to the problem modulo 109 + 7.

## Examples
```input
4 2
```
```output
11
```
-----
```input
7 7
```
```output
128
```

## Note
In the first sample the sequence ai looks as follows: (0, 1, 1, 0). All the possible subsequences are:

(), (0), (0, 0), (0, 1), (0, 1, 0), (0, 1, 1), (0, 1, 1, 0), (1), (1, 0), (1, 1), (1, 1, 0).

In the second sample the sequence ai looks as follows: (0, 1, 2, 3, 4, 5, 6). The subsequences of this sequence are exactly all increasing sequences formed from numbers from 0 to 6. It is easy to see that there are 27 = 128 such sequences.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
Little Susie loves strings. Today she calculates distances between them. As Susie is a small girl after all, her strings contain only digits zero and one. She uses the definition of Hamming distance:

We will define the distance between two strings s and t of the same length consisting of digits zero and one as the number of positions i, such that si isn't equal to ti.

As besides everything else Susie loves symmetry, she wants to find for two strings s and t of length n such string p of length n, that the distance from p to s was equal to the distance from p to t.

It's time for Susie to go to bed, help her find such string p or state that it is impossible.

## Input Format
The first line contains string s of length n.

The second line contains string t of length n.

The length of string n is within range from 1 to 105. It is guaranteed that both strings contain only digits zero and one.

## Output Format
Print a string of length n, consisting of digits zero and one, that meets the problem statement. If no such string exist, print on a single line "impossible" (without the quotes).

If there are multiple possible answers, print any of them.

## Examples
```input
0001
1011
```
```output
0011
```
-----
```input
000
111
```
```output
impossible
```

## Note
In the first sample different answers are possible, namely — 0010, 0011, 0110, 0111, 1000, 1001, 1100, 1101.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
Little Susie listens to fairy tales before bed every day. Today's fairy tale was about wood cutters and the little girl immediately started imagining the choppers cutting wood. She imagined the situation that is described below.

There are n trees located along the road at points with coordinates x1, x2, ..., xn. Each tree has its height hi. Woodcutters can cut down a tree and fell it to the left or to the right. After that it occupies one of the segments [xi - hi, xi] or [xi;xi + hi]. The tree that is not cut down occupies a single point with coordinate xi. Woodcutters can fell a tree if the segment to be occupied by the fallen tree doesn't contain any occupied point. The woodcutters want to process as many trees as possible, so Susie wonders, what is the maximum number of trees to fell.

## Input Format
The first line contains integer n (1 ≤ n ≤ 105) — the number of trees.

Next n lines contain pairs of integers xi, hi (1 ≤ xi, hi ≤ 109) — the coordinate and the height of the і-th tree.

The pairs are given in the order of ascending xi. No two trees are located at the point with the same coordinate.

## Output Format
Print a single number — the maximum number of trees that you can cut down by the given rules.

## Examples
```input
5
1 2
2 1
5 10
10 9
19 1
```
```output
3
```
-----
```input
5
1 2
2 1
5 10
10 9
20 1
```
```output
4
```

## Note
In the first sample you can fell the trees like that:

- fell the 1-st tree to the left — now it occupies segment [ - 1;1]
- fell the 2-nd tree to the right — now it occupies segment [2;3]
- leave the 3-rd tree — it occupies point 5
- leave the 4-th tree — it occupies point 10
- fell the 5-th tree to the right — now it occupies segment [19;20]

In the second sample you can also fell 4-th tree to the right, after that it will occupy segment [10;19].

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
The developers of Looksery have to write an efficient algorithm that detects faces on a picture. Unfortunately, they are currently busy preparing a contest for you, so you will have to do it for them.

In this problem an image is a rectangular table that consists of lowercase Latin letters. A face on the image is a 2 × 2 square, such that from the four letters of this square you can make word "face".

You need to write a program that determines the number of faces on the image. The squares that correspond to the faces can overlap.

## Input Format
The first line contains two space-separated integers, n and m (1 ≤ n, m ≤ 50) — the height and the width of the image, respectively.

Next n lines define the image. Each line contains m lowercase Latin letters.

## Output Format
In the single line print the number of faces on the image.

## Examples
```input
4 4
xxxx
xfax
xcex
xxxx
```
```output
1
```
-----
```input
4 2
xx
cf
ae
xx
```
```output
1
```
-----
```input
2 3
fac
cef
```
```output
2
```
-----
```input
1 4
face
```
```output
0
```

## Note
In the first sample the image contains a single face, located in a square with the upper left corner at the second line and the second column:

In the second sample the image also contains exactly one face, its upper left corner is at the second row and the first column.

In the third sample two faces are shown:

In the fourth sample the image has no faces on it.

Now solve the problem and return the code.