#include "boxes.h"
#include<bits/stdc++.h>
using namespace std;
///Partitions
///Determine the minimum distance that Adam has to travel to deliver all the souvenirs
///Subtask 4
///O(n^2)
///We have to partition the array into contiguous subsets of size k
///And one of size n%k
///We try all the possible rotations with the array (moving the start s)
///And the optimal has to be in one of that arrangements
///Since choosing not contiguous elements leads to bigger and overlapping subsets (we cannot leave gaps)
typedef long long ll;
int A[1000007];
int n;
int L;
ll sumRange(int s,int len) ///Return the cost of the range with start s and length len
{
ll cost=0;
int i=0;
int id=0;
while(i<len){
id=(i+s)%n;
if(i==0)
cost+=(ll)min(A[id],L-A[id]);
else{
int dist=abs(A[id]-A[(id+n-1)%n]);
cost+=(ll)min(dist,L-dist);
}
i++;
}
i--;
id=(i+s)%n;
cost+=(ll)min(A[id],L-A[id]);
return cost;
}
long long delivery(int N, int k, int l, int p[]) {
n=N;
L=l;
for(int i=0;i<n;i++){
A[i]=p[i];
}
ll minimum=LLONG_MAX;
for(int s=0;s<n;s++){ //For each possible start
ll cost=0;
if(n%k!=0) cost+=sumRange(s,n%k);
for(int i=n%k;i<n;i+=k){ //We build the subsets and compute the cost of each one
cost+=sumRange((s+i)%n,k);
}
minimum=min(minimum,cost);
}
return minimum;
}
