#include <bits/stdc++.h>
struct Line {
long long a, b;
int used;
constexpr std::pair <long long, int> f(long long x) const {
return { a * x + b, used };
}
};
struct LCT {
int size;
std::vector <std::pair <bool, Line>> lines;
LCT(int s) {
size = 1;
while (size < s) {
size <<= 1;
}
lines.resize(size << 1);
}
inline void reset() {
lines.assign(size << 1, { false, { 0, 1LL << 60, 0 } });
}
inline void insert(Line line) {
insert(line, 0, 0, size);
}
void insert(Line line, int now, int l, int r) {
int mid = (l + r) >> 1;
bool fl = !lines[now].first || line.f(l) < lines[now].second.f(l);
bool ml = !lines[now].first || line.f(mid) < lines[now].second.f(mid);
if (ml) {
std::swap(line, lines[now].second);
if (!lines[now].first) {
lines[now].first = true;
return;
}
}
if (r <= l + 1) {
return;
}
fl ^ ml ? insert(line, now * 2 + 1, l, mid) : insert(line, now * 2 + 2, mid + 1, r);
}
inline std::pair <long long, int> query(int x) {
return query(x, 0, 0, size);
}
std::pair <long long, int> query(int x, int now, int l, int r) {
if (!lines[now].first || r <= l + 1) {
return lines[now].first ? lines[now].second.f(x) : std::make_pair(1LL << 60, 0);
}
int mid = (l + r) >> 1;
return std::min(lines[now].second.f(x), x < mid ? query(x, now * 2 + 1, l, mid) : query(x, now * 2 + 2, mid + 1, r));
}
};
long long take_photos(int n, int m, int k, std::vector <int> _R, std::vector <int> _C) {
std::vector <std::pair <int, int>> a;
for (int i = 0; i < n; i++) {
a.emplace_back(_R[i], _C[i]);
if (_R[i] > _C[i]) {
std::swap(a.back().first, a.back().second);
}
}
std::sort(a.begin(), a.end(), [] (std::pair <int, int> u, std::pair <int, int> v) {
return u.first == v.first ? u.second > v.second : u.first < v.first;
});
int furth = -1;
for (int i = 0; i < n; i++) {
if (a[i].second > furth) {
furth = a[i].second;
a.emplace_back(a[i]);
}
}
a.erase(a.begin(), a.begin() + n);
n = a.size();
LCT lct(m);
auto f = [&] (long long mid, int& used) -> long long {
lct.reset();
#define add(val, use, poi) lct.insert({ (poi + 1) * -2, val + (long long) (poi + 1) * (poi + 1), use });
add(0, 0, a.back().second);
long long res = 0;
for (int i = n - 1; ~i; i--) {
std::pair <long long, int> now = lct.query(a[i].first);
used = now.second + 1;
res = now.first + mid + (long long) a[i].first * a[i].first;
if (i) {
res -= (long long) (a[i - 1].second + 1 - a[i].first) * (a[i - 1].second + 1 - a[i].first) * (a[i].first <= a[i - 1].second);
add(res, used, a[i - 1].second);
}
}
return res;
};
long long l = 0, r = 1LL << 60, best = 0;
while (l <= r) {
long long mid = (l + r) >> 1;
int used;
f(mid, used);
if (used > k) {
l = best = mid + 1;
} else {
r = mid - 1;
}
}
return f(best, furth) - best * k;
}
