#include "aliens.h"
#include <bits/stdc++.h>
//#define int ll
using namespace std;
#define ll long long
#define y1 zck_is_king
#define pii pair<ll, ll>
#define ull unsigned ll
#define f first
#define s second
#define ALL(x) x.begin(),x.end()
#define SZ(x) (int)x.size()
#define MN(a,b) a = min(a,(__typeof__(a))(b))
#define MX(a,b) a = max(a,(__typeof__(a))(b))
#define pb push_back
#define REP(i,n) for (int i = 0; i<n; ++i)
#define RREP(i,n) for (int i = n-1; i>=0; --i)
#define REP1(i,n) for (int i = 1; i<=n; ++i)
#define SORT_UNIQUE(c) (sort(c.begin(),c.end()), c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
#ifdef BALBIT
#define IOS()
#define bug(...) fprintf(stderr,"#%d (%s) = ",__LINE__,#__VA_ARGS__),_do(__VA_ARGS__);
template<typename T> void _do(T &&x){cerr<<x<<endl;}
template<typename T, typename ...S> void _do(T &&x, S &&...y){cerr<<x<<", ";_do(y...);}
#else
#define IOS() ios_base::sync_with_stdio(0);cin.tie(0);
#define endl '\n'
#define bug(...)
#endif
const int iinf = 1e9+10;
const ll inf = 1ll<<60;
const ll mod = 1e9+7 ;
void GG(){cout<<"0\n"; exit(0);}
ll mpow(ll a, ll n, ll mo = mod){ // a^n % mod
ll re=1;
while (n>0){
if (n&1) re = re*a %mo;
a = a*a %mo;
n>>=1;
}
return re;
}
ll inv (ll b, ll mo = mod){
if (b==1) return b;
return (mo-mo/b) * inv(mo%b,mo) % mo;
}
const int MM = 1e6+5;
const int NN = 1e5+5;
ll reach[MM]; // where does this point reach
ll over[NN]; // overcount for this index
ll dp[NN], take[NN];
ll at[NN], to[NN];
inline ll SQ(ll x) {return x*x;}
bool QTYPE = 0;
struct Line{
mutable ll m, b, p, id;
bool operator < (const Line &o) const {
if (QTYPE) return p < o.p;
return m < o.m;
}
};
struct LineContainer : multiset<Line> {
ll div(ll A, ll B) {
return A/B - ((A%B) && ((A^B)<0));
}
bool isect (iterator x, iterator y) {
if (y == end()) {
x->p = inf; return false;
}
if (x->m == y->m) {
x->p = x->b > y->b? inf : -inf;
}else{
x->p = div(x->b - y->b, y->m - x->m);
}
return x->p >= y->p;
}
void add(ll m, ll b, int id) {
m=-m; b=-b;
auto z = insert({m,b,0,id}), y = z++, x = y;
while (isect(y,z)) z = erase(z);
if (x!=begin() && isect(--x, y)) {
isect(x, y = erase(y));
}
while ((y=x)!=begin() && (--x)->p >= y->p) {
isect(x, erase(y));
}
}
pii query(ll x) {
QTYPE = 1;
auto it = lower_bound({0,0,x,-1});
ll ret = it->m * x + it->b;
QTYPE = 0;
return {-ret, it->id};
}
};
pii brute(int n,ll pen) { // pen is (positive) penalty for each thing chosen
LineContainer CV;
REP(i,n+1) {
if (i!=n && at[i] > to[i+1]) {
over[i] = SQ(at[i] - to[i+1]);
}
if (i) {
pii yo = CV.query(at[i]);
dp[i] = yo.f + pen + SQ(at[i]);
take[i] = take[yo.s]+1;
bug(i, dp[i], take[i]);
}
CV.add(-2 * to[i+1], SQ(to[i+1]) - over[i] + dp[i], i);
}
return pii{dp[n], take[n]};
}
long long take_photos(int n, int m, int k, std::vector<int> ROW, std::vector<int> COL) {
ll re = 0;
memset(reach, 0x3f, sizeof reach);
REP(i,n) {
int a = ROW[i], b = COL[i];
if (a > b) swap(a,b);
MN(reach[b], a);
}
int nowdep = (0x3f3f3f3f)-1;
vector<pii> use;
for (int i = m-1; i>=0; --i) {
if (reach[i] < nowdep) {
nowdep = reach[i];
use.emplace_back(i, reach[i]);
bug(i, reach[i]);
}
}
reverse(ALL(use));
bug (SZ(use));
at[0] = to[0] = -1;
REP(i, SZ(use)){
at[i+1] = use[i].f;
to[i+1] = use[i].s-1;
}
{
ll l = 0, r = 1e13;
while (l!=r) {
ll mid = (l+r)/2;
pii hi = brute(SZ(use), mid);
if (hi.s > k) {
// taking too many! penalize!!!
l = mid+1;
}else{
r = mid;
}
}
bug(l);
pii go = brute(SZ(use), l);
ll re = (go.s) * -l - (k-go.s)*l + go.f;
bug(re, go.f, go.s);
return re;
}
}
//signed main(){
// ll r = take_photos(5, 7, 1, vector<int>{0, 4, 4, 4, 4}, vector<int>{3, 4, 6, 5, 6});
// cout<<r<<endl;
//}
//
//signed main(){
//
//}
