Map

Memory limit: 32 MB

After a new administrative division of Byteland cartographic office works on a new demographic map of the country. Because of technical reasons only a few colors can be used. The map should be colored so that regions with the same or similar population (number of inhabitants) have the same color. For a given color let be the number, such that:

• at least half of regions with color has population not greater than
• at least half of regions with color has population not less than

A coloring error of a region marked with color is an absolute value of the difference between and the region's population. A cumulative error is a sum of coloring errors of all regions. We are looking for an optimal coloring of the map (the one with the minimal cumulative error).

Task

Write a program which:

• reads the population of regions in Byteland from the standard input,
• computes the minimal cumulative error,
• writes the result to the standard output.

Input

In the first line of the standard input an integer is written, which is the number of regions in Byteland, . In the second line the number denoting the number of colors used to color the map is written, . In each of the following lines there is one non-negative integer - a population of one of the regions of Byteland. No population exceeds .

Output

Your program should write in the only line of the standard output one integer number equal to a minimal cumulative error, which can be achieved while the map is colored (optimally).

Example

For the input data:

11
3
21
14
6
18
10
2
15
12
3
2
2

the correct result is:

15

Task author: Marcin Sawicki.