The fastfood chain McBurger owns several restaurants along a highway. Recently, they have decided to build several depots along the highway, each one located at a restaurent and supplying several of the restaurants with the needed ingredients. Naturally, these depots should be placed so that the average distance between a restaurant and its assigned depot is minimized. You are to write a program that computes the optimal positions and assignments of the depots. To make this more precise, the management of McBurger has issued the following specification: You will be given the positions of n restaurants along the highway as n integers d₁ < d₂ <...< d_n (these are the distances measured from the company's headquarter, which happens to be at the same highway). Furthermore, a number k (k <= n) will be given, the number of depots to be built. The k depots will be built at the locations of k different restaurants. Each restaurant will be assigned to the closest depot, from which it will then receive its supplies. To minimize shipping costs, the total distance sum, defined as n Σ |d_i-(position of depot serving restaurant i)| i=1 must be as small as possible. Write a program that computes the positions of the k depots, such that the total distance sum is minimized.

The input file contains several descriptions of fastfood chains. Each description starts with a line containing the two integers n and k. n and k will satisfy 1 <= n <= 200 , 1 <= k <= 30 , k <= n. Following this will n lines containing one integer each, giving the positionsdi of the restaurants, ordered increasingly. The input file will end with a case starting with n = k = 0. This case should not be processed.

For each chain, first output the number of the chain. Then output a line containing the total distance sum. Output a blank line after each test case.

Southwestern European Regional Contest 1998