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.
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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 
(these are the distances measured from the company's headquarter, which happens to be at the same highway). Furthermore, a number 
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
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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.
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Input
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
,
,
. Following this will n lines containing one integer each, giving the positions d
i of the restaurants, ordered increasingly.
The input file will end with a case starting with n = k = 0. This case should not be processed.
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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.
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Output a blank line after each test case.
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Sample Input
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6 3
5
6
12
19
20
27
0 0
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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
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考虑dp状态为dp[i][j]:前i个酒店建k个仓库的最小代价。 dp[i][j]=min(dp[k][j-1]+dis[k+1][i])(j-1<=k
关于路径输出设path[i][j]为达到dp[i][j]状态的前一状态的末仓库。 易知道path[i][1]=0; 其他的就是递归输出了。
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