//#include "grader.cpp"
#include "boxes.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimize("Ofast,unroll-loops")
using namespace std;
using namespace __gnu_pbds;
#define pb push_back
#define all(x) x.begin(),x.end()
#define ar array
#define mrand(a, b) uniform_int_distribution<int>(a, b)(rng)
template<class T>bool umax(T &a,T b){if(a<b){a=b;return true;}return false;}
template<class T>bool umin(T &a,T b){if(b<a){a=b;return true;}return false;}
template<class T> using ste = tree<T, null_type, less_equal<T>,
rb_tree_tag, tree_order_statistics_node_update>;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
const long long inf = 1e17 + 7;
const int mod = 1e9 + 7;
const int N = 1e7 + 5;
const int md = 998244353;
int binpow(int a, int b, int m){
if(b == 0)return 1;
if(b % 2 == 0){
int c = binpow(a,b/2,m);
return (c*c)%m;
}
return (binpow(a,b-1,m)*a)%m;
}
int divi(int a, int b, int m){
return (a*(binpow(b,m-2, m)))%m;
}
long long delivery(int N, int K, int L, int p[]){
vector<long long>pref(N, inf), suff(N, inf);
for(int i = 0;i<N;i++){
if(i < K)pref[i] = p[i];
else pref[i] = pref[i-K] + p[i-K] + p[i];
}
vector<int>dis(N);
for(int i = 0;i<N;i++){
dis[i] = L - p[i];
}
for(int i = N-1;i>=0;i--){
if(i + K >= N)suff[i] = dis[i];
else suff[i] = suff[i+K] + dis[i+K] + dis[i];
}
long long res = inf;
for(int i = 0;i<N;i++){
if(i == 0)
umin(res, suff[i] + min(p[i], dis[i]));
if(i == N-1)
umin(res, pref[i] + min(p[i], dis[i]));
if(i < N-1){
umin(res, pref[i] + suff[i+1] + min(p[i], dis[i]) + min(dis[i+1], p[i+1]));
}
}
return res;
}
