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 k let A(k) be the number, such that: 

• at least half of regions with color k has population not greater than A(k)
• at least half of regions with color k has population not less than A(k) 

A coloring error of a region is an absolute value of the difference between A(k) 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 input file MAP.IN,
• computes the minimal cumulative error,
• writes the result in the text file MAP.OUT.

Input

In the first line of the input file MAP.IN an integer n is written, which is the number of regions in Byteland, 10< n <3000. In the second line the number m denoting the number of colors used to color the map is written, 2 <= m <= 10. In each of the following n lines there is one non-negative integer - a population of one of the regions of Byteland. No population exceeds 2^30. 

Output

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

Example

For the input file MAP.IN:

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

15