#include "boxes.h"
/*
ID: awesome35
LANG: C++14
TASK: vans
*/
#define _CRT_SECURE_NO_WARNINGS
#include<bits/stdc++.h>
#include<unordered_set>
#include<unordered_map>
#include<chrono>
using namespace std;
typedef pair<int, int> pii;
typedef long long ll;
typedef pair<ll, ll> pll;
typedef long double ld;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<pair<int, int>> vpi;
typedef vector<pair<ll, ll>> vpll;
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
#define pb push_back
#define mp make_pair
#define rsz resize
#define sz(x) int(x.size())
#define all(x) x.begin(),x.end()
#define f first
#define s second
#define cont continue
#define endl '\n'
#define ednl '\n'
#define test int testc;cin>>testc;while(testc--)
#define pr(a, b) trav(x,a)cerr << x << b; cerr << endl;
#define message cout << "Hello World" << endl;
//const int dx[4] = { 1,0,-1,0 }, dy[4] = { 0,1,0,-1 }; // for every grid problem!!
const ll linf = 4000000000000000000LL;
const ll inf = 1000000007;//998244353
const ld pi = 3.1415926535;
void pv(vi a) { trav(x, a)cout << x << " "; cout << endl; }void pv(vll a) { trav(x, a)cout << x << " "; cout << endl; }void pv(vector<vi>a) {
F0R(i, sz(a)) { cout << i << endl; pv(a[i]); cout << endl; }
}void pv(vector<vll>a) { F0R(i, sz(a)) { cout << i << endl; pv(a[i]); }cout << endl; }void pv(vector<string>a) { trav(x, a)cout << x << endl; cout << endl; }
void setIO(string s) {
ios_base::sync_with_stdio(0); cin.tie(0);
if (sz(s))
{
freopen((s + ".in").c_str(), "r", stdin);
if (s != "ioi")
freopen((s + ".out").c_str(), "w", stdout);
}
}
const int MAX = 100;
int n, k, L;
vi a;
ll sub1()
{
ll ans = 0;
trav(x, a)
{
ans += min(x, L - x);
}
ans *= 2;
return ans;
}
ll sub2()
{
int ans = inf;
ans = L;
ans = min(ans, 2 * a[n - 1]);
ans = min(ans, 2 * (L - a[0]));
F0R(i, n - 1)
{
ans = min(ans, 2 * (a[i] + L - a[i + 1]));
}
return ans;
}
int popcount(int a)
{
int count = 0;
while (a)
{
count += (a & 1);
a >>= 1;
}
return count;
}
ll sub3()
{
int total = 1 << n;
vll dp(total, linf);
dp[0] = 0;
F0R(mask, total)
{
if (dp[mask] == linf)continue;
F0R(nmask, total)
{
if (popcount(nmask) > k || popcount(nmask) == 0)continue;
if (mask & nmask)continue;
int cost = L;
vi b;
F0R(i, n)if (nmask & (1 << i))b.pb(a[i]);
cost = min(cost, 2 * b[sz(b) - 1]);
cost = min(cost, 2 * (L - b[0]));
F0R(i, sz(b) - 1)
{
cost = min(cost, 2 * (b[i] + L - b[i + 1]));
}
dp[mask | nmask] = min(dp[mask | nmask], dp[mask] + cost);
}
}
return dp[total - 1];
}
ll sub4()
{
vll dp(n + 1, linf);
dp[0] = 0;
F0R(i, n)
{
FOR(j, 1, k + 1)
{
if (i + j > n)break;
int cost = L;
cost = min(cost, 2 * a[i + j - 1]);
cost = min(cost, 2 * (L - a[i]));
dp[i + j] = min(dp[i + j], dp[i] + cost);
}
}
return dp[n];
}
struct T
{
unordered_multiset<ll> todo;
priority_queue<ll, vll, greater<ll>>x;
void insert(ll t)
{
x.push(t);
}
void erase(ll t)
{
todo.insert(t);
}
ll get()
{
while (sz(x))
{
ll temp = x.top();
if (todo.find(temp) != todo.end())todo.erase(todo.find(temp)), x.pop();
else
{
return temp;
}
}
assert(0);
return 0123123;
}
};
ll sub56()
{
vll dp(n + 1, linf);
dp[0] = 0;
T val1, val2;// stores min 2 * L + dp[i] - 2 * a[i] and stores min dp[i]. remeber to + min(L, 2 * a[i - 1])
val1.insert(2 * (L - a[0]));
val2.insert(0);
FOR(i, 1, n + 1)
{
/*
FOR(j, i - k, i)
{
if (j < 0)continue;
dp[i] = min({ dp[i], dp[j] + 2 * (L - a[j]), dp[j] + min(L, 2 * a[i - 1]) });
}*/
dp[i] = min(val1.get(), val2.get() + min(L, 2 * a[i - 1]));
if (i >= k)
{
val1.erase(dp[i - k] + 2 * (L - a[i - k]));
val2.erase(dp[i - k]);
}
if (i < n)
{
val1.insert(dp[i] + 2 * (L - a[i]));
val2.insert(dp[i]);
}
}
return dp[n];
}
ll delivery(int A, int b, int c, int* d)
{
n = A, k = b, L = c;
a.rsz(n);
F0R(i, n)a[i] = d[i];
if (n <= 1000)
{/*
if (k == 1)
{
return sub1();
}
else if (k == n)
{
return sub2();
}
else if (n <= 10)
{
return sub3();
}
return sub56();*/
}
return sub56();
}
