#include <stdio.h>
#include <algorithm>
#include <string.h>
#include <vector>
#include <utility>
#include "aliens.h"
#define N 100100
#define M 1001000
#define ll long long
#define ii std::pair<long long,long long>
#define il std::pair<long long,int>
#define lp std::pair<long long, long long>
#define lpp std::pair<std::pair<long long, long long>,int>
ll over[N];
int line[M];
std::vector<ii> pt;
std::vector<il> dp(N);
lpp que[N];
int ql;
ll minl(ll a, ll b){
if(a == -1)return b;
if(b == -1)return a;
return a < b ? a:b;
};
double intersect(lpp ln1, lpp ln2){
ll f = ln2.first.second - ln1.first.second;
ll s = ln1.first.first - ln2.first.first;
return (double)f/double(s);
};
void insertQue(lpp ln){
while(ql >= 2){
double f1 = intersect(ln,que[ql-1])+1;
double f2 = intersect(ln,que[ql-2])+1;
if(f2 >= f1){
ql--;
}else break;
};
que[ql++] = ln;
};
il findQue(ll x){
int l = 0;
int r = ql;
while(l < r){
int m = (l+r)>>1;
ll f1 = -1;
ll f2 = -1;
if(m > 0){
f1 = intersect(que[m],que[m-1])+1;
};
if(m < ql-1){
f2 = intersect(que[m],que[m+1]);
};
if(m == 0 && m == ql-1){
l = m;
break;
};
if(m == 0 && m < ql-1 && f2 >= x){
if(f2 >= x){
l = m;
break;
}else{
l = m+1;
};
};
if(m == ql-1 && m > 0){
if(f1 <= x){
l = m;
break;
}else{
r = m;
};
};
if(m > 0 && m < ql-1){
if(f1 <= x && x <= f2){
l = m;
break;
}else if(f1 > x){
r = m;
}else if(f2 < x){
l = m+1;
};
};
};
return il(que[l].first.first * x + que[l].first.second,que[l].second+1);
};
void solvecv(ll c){
ql = 0;
dp[0].first = 0;
dp[0].second = 0;
insertQue(lpp(lp(-2*pt[0].first,pt[0].first * pt[0].first - over[0] * over[0] + c + dp[0].first),dp[0].second));
ll c1;
for(int i = 1;i<pt.size();i++){
if(over[i])c1 = over[i] + pt[i].first;
else c1 = std::max(over[i-1],(ll)pt[i-1].second) + pt[i-1].first;
dp[i] = findQue(c1);
dp[i].first += c1 * c1;
//printf("%lld %lld %d\n",c1,dp[i].first,dp[i].second);
insertQue(lpp(lp(-2*pt[i].first,pt[i].first * pt[i].first - over[i] * over[i] + c + dp[i].first),dp[i].second));
};
};
ll solvebn(ll m, ll k){
ll l = 0;
ll r = m * m + 1;
ll md;
ll kl = 1;
ll kr = pt.size();
while(l < r){
md = (l+r)>>1ll;
solvecv(md);
int tk = dp[pt.size()-1].second;
if(tk == k){
return dp[pt.size()-1].first - k * md;
};
if(tk > k){
l = md+1;
kr = tk;
}else{
r = md;
kl = tk;
};
};
solvecv(r+1);
ll tm1 = dp[pt.size()-1].first - (r+1) * kl;
solvecv(l);
ll tm2 = dp[pt.size()-1].first - l * kr;
ll tm3 = (tm1-tm2) / (kr-kl);
return tm1 - (k-kl) * tm3;
};
ll take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c){
memset(over,0,sizeof(over));
memset(line,0,sizeof(line));
pt.clear();
for(int i = 0;i<n;i++){
if(r[i] >= c[i]){
line[c[i]] = std::max(line[c[i]],r[i]-c[i]+1);
}else if(r[i] < c[i]){
line[r[i]] = std::max(line[r[i]],c[i]-r[i]+1);
};
};
for(int i = 0;i<m;i++){
if(line[i])pt.push_back(ii(i,line[i]));
};
for(int i = 1;i<pt.size();i++){
if(over[i-1] > pt[i-1].second){
over[i] = over[i-1] + pt[i-1].first - pt[i].first;
}else{
over[i] = pt[i-1].second + pt[i-1].first - pt[i].first;
};
if(over[i] < 0)over[i] = 0;
//printf("pt: %d %d %d\n",pt[i].first,pt[i].second,over[i]);
};
over[pt.size()] = 0;
pt.push_back({0,0});
//printf("%d %d %d %d\n",pt.size(),pt[0].first,pt[0].second,over[0]);
return solvebn(m,k);
};
