##### Canadian Computing Competition: 2010 Stage 1, Senior #3

There is a very unusual street in your neighbourhood. This street forms a perfect circle, and the circumference of the circle is . There are () houses on the street. The address of each house is the clockwise arc-length from the northern-most point of the circle. The address of the house at the northern-most point of the circle is .

You also have special firehoses which follow the curve of the street. However, you wish to keep the length of the longest hose you require to a minimum.

Your task is to place () fire hydrants on this street so that the maximum length of hose required to connect a house to a fire hydrant is as small as possible.

#### Input Specification

The first line of input will be an integer , the number of houses. The next lines each contain one integer, which is the address of that particular house, and each house address is at least and less than . On the nd line is the number , which is the number of fire hydrants that can be placed around the circle. Note that a fire hydrant can be placed at the same position as a house. You may assume that no two houses are at the same address. Note: at least 40% of the marks for this question have .

#### Output Specification

On one line, output the minimum integral length of hose required so that every house can connect to its nearest fire hydrant with that length of hose.

#### Sample Input

```
4
0
67000
68000
77000
2
```

#### Output for Sample Input

`5000`

## Comments

The problem does not specify whether the location of each fire hydrant has to be an integer and whether the length of the hoses can contain a decimal. This should be added to the question as some of the solutions are different if you assume that the lengths and positions are not limited to integers.

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How would you use binary search on multiple hydrants?

Not sure if this fits here, but for anyone who wants to practice binary search, here's some good ones: https://codeforces.com/edu/course/2/lesson/6/2/practice

There's some video explanations here: https://codeforces.com/edu/course/2/lesson/6/2

water is wet.

Can the length of the hoses contain decimals?

I think it can be shown that the only decimal will be point 5, in which case I think you just round up.

The original CEMC test data is now worth 80% of the marks. New cases, worth the remaining 20%, have been added.

All submissions have been rejudged.