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 (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

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 , , . 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.

## 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

6 3 5 6 12 19 20 27 0 0

## 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

#include<cstdio> #include<cstring> #include<algorithm> #define mem(name,value) memset(name,value,sizeof(name)) #define FOR(i,n) for(int i=1;i<=n;i++) using namespace std; const int maxn = 200+10; const int maxk = 30+10; const int inf = 0x3f3f3f3f; int d[maxk][maxn],des[maxn],a1[maxk]; typedef pair<int,int>pii; pii p[maxk][maxn],p1[maxk]; int dp(int cnt,int n){ if(d[cnt][n]!=-1) return d[cnt][n]; int &ans = d[cnt][n]; if(cnt==0) return ans = (n ? inf : 0); ans = inf; for(int i=cnt;i<=n;i++){ int len = (n-i)/2, v = i+len; int s = 0; for(int j=v+1;j<=n;j++) s += des[j] - des[v]; for(int j=v-1;j>=i;j--) s += des[v] - des[j]; int tmp = dp(cnt-1,i-1) + s; if(tmp < ans){ ans = tmp; p[cnt][n] = make_pair(i,v); } } return ans; } void print_ans(int cnt,int n){ if(cnt==0) return ; a1[cnt] = p[cnt][n].second; p1[cnt] = make_pair(p[cnt][n].first,n); print_ans(cnt-1,p1[cnt].first-1); } int main(){ //freopen("in.txt","r",stdin); //freopen("out2.txt","w",stdout); int n,k,kase=0; while(~scanf("%d%d",&n,&k) && n){ printf("Chain %d\n",++kase); mem(d,-1); des[0] = 0; for(int i=1;i<=n;i++){ scanf("%d",&des[i]); } int solve = dp(k,n); print_ans(k,n); for(int i=1;i<=k;i++){ printf("Depot %d at restaurant %d serves ",i,a1[i]); if(p1[i].first==p1[i].second) printf("restaurant %d\n",p1[i].first); else printf("restaurants %d to %d\n",p1[i].first,p1[i].second); } printf("Total distance sum = %d\n\n",solve); } return 0; }