#include "aliens.h"
#include <bits/stdc++.h>
using ll = long long;
using namespace std;
inline ll square(ll x) { return x*x; }
int n, m, k;
vector<ll> l, r;
void tidy_up() {
for(int i = 0; i < n; i++) if(l[i] > r[i]) swap(l[i], r[i]);
vector<ll> id(n);
iota(id.begin(), id.end(), 0);
sort(id.begin(), id.end(), [] (int i, int j) {
return make_pair(r[i], -l[i]) < make_pair(r[j], -l[j]);
});
vector<ll> tmp;
tmp.push_back(-1);
tmp.push_back(id[0]);
for(int i = 1; i < n; i++) {
while(tmp.size() > 1 && l[tmp.back()] >= l[id[i]]) tmp.pop_back();
tmp.push_back(id[i]);
}
n = tmp.size() - 1;
id = tmp;
for(int i = 1; i <= n; i++) tmp[i] = r[id[i]];
r = tmp;
for(int i = 1; i <= n; i++) tmp[i] = l[id[i]];
l = tmp;
}
struct cht {
struct line {
ll m, c;
int cnt;
line(ll m, ll c, int cnt): m(m), c(c), cnt(cnt) {};
ll getVal(ll x) { return m*x + c; }
};
vector<line> f;
int idx;
bool bad(line l1, line l2, line l3) { // m1 >= m2 >= m3
assert(l1.m >= l2.m && l2.m >= l3.m);
return (double) (l1.c-l3.c)*(l2.m-l1.m) <= (double) (l1.c-l2.c)*(l3.m-l1.m);
}
void update(ll m, ll c, int cnt) {
line l = line(m, c, cnt);
while(f.size() >= 2 && bad(f[f.size()-2], f[f.size()-1], l)) f.pop_back();
f.push_back(l);
}
pair<ll, int> query(ll x) {
while(idx+1 < f.size() && f[idx+1].getVal(x) < f[idx].getVal(x)) ++idx;
return make_pair(f[idx].getVal(x), f[idx].cnt);
}
void clear() { f.clear(); idx = 0; }
} hull;
pair<ll, int> calc(ll C) {
vector<pair<ll, int> > dp = vector<pair<ll, int> >(n+1);
hull.clear();
dp[0] = {0, 0};
hull.update(-2*(l[1]-1), square(l[1]-1), 0);
for(int i = 1; i <= n; i++) {
auto tmp = hull.query(r[i]);
dp[i].first = tmp.first + square(r[i]) + C;
dp[i].second = tmp.second + 1;
if(i == n) break;
hull.update(-2*(l[i+1]-1), square(l[i+1]-1) + dp[i].first - square(max(0ll, r[i] - l[i+1] + 1)), dp[i].second);
}
return dp[n];
}
ll take_photos(int _n, int _m, int _k, vector<int> _l, vector<int> _r) {
n = _n, m = _m, k = _k;
l.resize(n), r.resize(n);
for(int i = 0; i < n; i++) l[i] = _l[i], r[i] = _r[i];
tidy_up();
ll s = 0, e = 1e17;
while(s < e) {
ll mid = s+e >> 1;
if(calc(mid).second <= k) e = mid;
else s = mid+1;
}
return calc(s).first - s * k;
}
