Supply depots

A grocery chain owns several stores along a road. They wish to build several depots along the road, each one located at a store and supplying several of the stores with materials. Naturally, these depots should be placed so that the average distance between a store and its assigned depot is minimized. You are to write a program that computes the optimal positions and assignments of the depots.


More formally, you are given the positions of n stores along the highway as n integers $d_1 < d_2 < \dots < d_n$ (these are the distances measured from the company's headquarter, which happens to be on the same road). Furthermore, a number $k (k \leŸ n)$ will be given, the number of depots to be built. The k depots will be built at the locations of k different stores. Each store will be assigned to the closest depot, from which it will then receive its supplies. To minimize transportation costs, the distance sum, defined as


\begin{displaymath}\sum_{i=1}^n \mid d_i - (\mbox{position of depot serving restaurant }i) \mid \end{displaymath}

must be as small as possible. Write a program that computes the positions of the k depots, such that this sum is minimized.

Input 

The input file contains several descriptions of  chains. Each description starts with a line containing the two integers n and k. n and k will satisfy $1 \leŸ n \leŸ 200$ , $1 \leŸ k Ÿ\le 30$ , $k \le n$ . Following this will n lines containing one integer each, giving the positions di of the stores, ordered increasingly.

The input file will end with a case starting with n = k = 0. This case should not be processed.

Output 

For each chain, first output the number of the chain. Then output  the total distance sum, as defined in the problem text.

.

Sample Input  

6 3
5
6
12
19
20
27
0 0

Sample Output  

Chain 1 : Total distance sum = 8.