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    <TD align=right>Time limit:</TD>
    <TD width=50>3sec.</TD>
    <TD align=right>Submitted:</TD>
    <TD width=50>863</TD></TR>
  <TR>
    <TD align=right>Memory limit:</TD>
    <TD width=50>32M</TD>
    <TD align=right>Accepted:</TD>
    <TD width=50>208</TD></TR></TBODY></TABLE></CENTER>
<CENTER>Source : <A
href="http://acm.hit.edu.cn/ojs/result.php?str=%22Unknown%22"><FONT
color=red>Unknown</FONT></A></CENTER>
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      <P>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 restaurant 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.</P>
      <P>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 &lt; d2 &lt; ... &lt; dn (these are the
      distances measured from the company's headquarter, which happens to be at
      the same highway). Furthermore, a number k (k &lt;= n) will be given, the
      number of depots to be built. </P>
      <P>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</P>
      <CENTER><IMG src="http://acm.hit.edu.cn/ojs/pic/1005_a.gif"></CENTER>
      <P>must be as small as possible.</P>
      <P>Write a program that computes the positions of the k depots, such that
      the total distance sum is minimized. </P><B>Input</B><BR>
      <P>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 &lt;= n &lt;= 200, 1 &lt;= k &lt;= 30, k &lt;= n.
      Following this will n lines containing one integer each, giving the
      positions di of the restaurants, ordered increasingly.</P>
      <P>The input file will end with a case starting with n = k = 0. This case
      should not be processed. </P><B>Output</B><BR>
      <P>For each chain, first output the number of the chain. Then output a
      line containing the total distance sum. </P>
      <P>Output a blank line after each test case. </P><B>Sample Input </B><BR><PRE>6 3
5
6
12
19
20
27
0 0
</PRE><B>Sample Output</B><BR><PRE>Chain 1
Total distance sum = 8

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Time limit: 3sec. Submitted: 863
Memory limit: 32M Accepted: 208

Source : Unknown

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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 restaurant 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

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 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 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 a line containing the total distance sum.

Output a blank line after each test case.

Sample Input

6 3
5
6
12
19
20
27
0 0

Sample Output

Chain 1
Total distance sum = 8