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 < · · · < dn (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 | di − (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. Input The input file contains several descriptions of fastfood chains. Each description starts with a line containingthetwointegersnandk. nandkwillsatisfy1≤n≤200,1≤k≤30,k≤n. Followingthis will n lines containing one integer each, giving the positions di of the restaurants, 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 an optimal placement of the depots as follows: for each depot output a line containing its position and the range of restaurants it serves. If there is more than one optimal solution, output any of them. After the depot descriptions output a line containing the total distance sum, as defined in the problem text. Output a blank line after each test case. Sample Input 63 5 6 12 19 20 27 00
2/2 Sample Output Chain 1 Depot 1 at restaurant 2 serves restaurants 1 to 3 Depot 2 at restaurant 4 serves restaurants 4 to 5 Depot 3 at restaurant 6 serves restaurant 6 Total distance sum = 8