The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

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geometry

greedy

*2600

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D. King's Problem?

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputEvery true king during his life must conquer the world, hold the Codeforces world finals, win pink panda in the shooting gallery and travel all over his kingdom.

King Copa has already done the first three things. Now he just needs to travel all over the kingdom. The kingdom is an infinite plane with Cartesian coordinate system on it. Every city is a point on this plane. There are *n* cities in the kingdom at points with coordinates (*x*_{1}, 0), (*x*_{2}, 0), ..., (*x*_{n}, 0), and there is one city at point (*x*_{n + 1}, *y*_{n + 1}).

King starts his journey in the city number *k*. Your task is to find such route for the king, which visits all cities (in any order) and has minimum possible length. It is allowed to visit a city twice. The king can end his journey in any city. Between any pair of cities there is a direct road with length equal to the distance between the corresponding points. No two cities may be located at the same point.

Input

The first line contains two integers *n* and *k* (1 ≤ *n* ≤ 10^{5}, 1 ≤ *k* ≤ *n* + 1) — amount of cities and index of the starting city. The second line contains *n* + 1 numbers *x*_{i}. The third line contains *y*_{n + 1}. All coordinates are integers and do not exceed 10^{6} by absolute value. No two cities coincide.

Output

Output the minimum possible length of the journey. Your answer must have relative or absolute error less than 10^{ - 6}.

Examples

Input

3 1

0 1 2 1

1

Output

3.41421356237309490000

Input

3 1

1 0 2 1

1

Output

3.82842712474619030000

Input

4 5

0 5 -1 -5 2

3

Output

14.24264068711928400000

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