#include <bits/stdc++.h>
#ifndef LOCAL
#include "aliens.h"
#endif
using namespace std;
struct Line {
int a;
long long b;
Line() {}
Line(int _a, long long _b) {
a = _a, b = _b;
}
long long f(int x) {
return a * 1ll * x + b;
}
~Line() {}
};
int sign(long long x) {
if (x > 0) { return 1; }
if (x < 0) { return -1; }
return 0;
}
long long intersect(const Line& A, const Line& B) {
// x = (B.b - A.b) / (A.a - B.a)
long long numer = B.b - A.b, denom = A.a - B.a;
int sn = sign(numer), sd = sign(denom);
numer *= sn, denom *= sd;
if (sn * sd < 0) {
return numer / denom * -1;
}
return (numer + denom - 1) / denom;
}
long long take_photos(int n, int m, int k, vector<int> rows, vector<int> cols) {
vector<int> maxRight(m, -1);
for (int i = 0; i < n; ++i) {
int l = min(rows[i], cols[i]);
int r = max(rows[i], cols[i]);
maxRight[l] = max(maxRight[l], r + 1);
}
vector<pair<int, int>> segs;
for (int l = 0; l < m; ++l) {
if (maxRight[l] != -1 && (segs.empty() || segs.back().second < maxRight[l])) {
segs.emplace_back(l, maxRight[l]);
}
}
n = segs.size();
/*for (const auto& [l, r] : segs) {
cerr << l << ' ' << r << '\n';
}*/
k = min(k, n);
vector<pair<long long, int>> dp(n);
vector<Line> lines;
vector<long long> optX;
vector<int> cntSegs;
auto compute = [&](long long lambda) -> int {
lines = {};
optX = {};
cntSegs = {};
dp[0] = {(segs[0].second - segs[0].first) * 1ll * (segs[0].second - segs[0].first) + lambda, 1};
for (int i = 1, ptr = 0; i < n; ++i) {
// cerr << "i: " << i << '\n';
int lenInter = max(0, segs[i - 1].second - segs[i].first);
Line l(-2 * segs[i].first, dp[i - 1].first - lenInter * 1ll * lenInter + segs[i].first * 1ll * segs[i].first);
while (!lines.empty() && intersect(lines.back(), l) <= optX.back()) {
optX.pop_back();
lines.pop_back();
cntSegs.pop_back();
}
if (!lines.empty()) {
optX.emplace_back(intersect(lines.back(), l));
} else {
optX.emplace_back(-1);
}
lines.emplace_back(l);
cntSegs.emplace_back(dp[i - 1].second);
// cerr << "inserted!\n";
ptr = min(ptr, (int)lines.size() - 1);
while (ptr + 1 < (int)lines.size() && optX[ptr + 1] <= segs[i].second) {
++ptr;
}
// cerr << "found!\n";
dp[i] = {lines[ptr].f(segs[i].second) + segs[i].second * 1ll * segs[i].second + lambda, cntSegs[ptr] + 1};
if ((segs[i].second - segs[0].first) * 1ll * (segs[i].second - segs[0].first) + lambda < dp[i].first) {
dp[i] = {(segs[i].second - segs[0].first) * 1ll * (segs[i].second - segs[0].first) + lambda, 1};
}
// cerr << "i: " << i << ", dp: " << dp[i].first << ' ' << dp[i].second << '\n';
}
return dp[n - 1].second;
};
long long left = -1, right = m * 1ll * m + 10;
while (right - left > 1) {
long long mid = left + (right - left) / 2;
// cerr << "mid: " << mid << '\n';
int res = compute(mid);
// cerr << "res: " << res << '\n';
if (res >= k) {
left = mid;
} else {
right = mid;
}
}
compute(left);
// cerr << "right: " << right << '\n';
// cerr << "dp: " << dp[n - 1].first << ", " << dp[n - 1].second << '\n';
return dp[n - 1].first - k * left;
}
/*
void solve() {
int n, m, k;
cin >> n >> m >> k;
vector<int> r(n), c(n);
for (int i = 0; i < n; ++i) {
cin >> r[i] >> c[i];
}
cout << take_photos(n, m, k, r, c) << '\n';
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
#ifdef LOCAL
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
int T = 1;
cin >> T;
while (T--) {
solve();
cerr << "-----------\n";
cout << "-----------\n";
}
#else
int T = 1;
cin >> T;
while (T--) {
solve();
}
#endif
return 0;
}
*/
