#include "aliens.h"
#include<bits/stdc++.h>
using namespace std;
#define int long long
const int INF = 1e18;
pair<int,int> v[100005],newv[100005];
struct line
{
int b,m;
int eval(int x){ return m*x + b; }
};
double interx(line u, line v)
{
return (double)(v.b - u.b)/(double)(u.m - v.m);
}
pair<int,int> calc(int n, int k, int coef)
{
vector<pair<int,int>> dp(n+2,{INF,0});
dp[0]={0,0};
deque<pair<line,int>> hull;
for(int i=1;i<=n;i++)
{
int u=i-1;
line cur;
if(v[u+1].second > v[u].first)
{
cur.b = dp[u].first + v[u+1].second*v[u+1].second + 1;
cur.m = -2*v[u+1].second;
}
else
{
cur.b = dp[u].first + 2*v[u+1].second * (v[u].first+1) - v[u].first*(v[u].first+2);
cur.m = -2*v[u+1].second;
}
while((int)hull.size()>1 && interx(hull.back().first,cur) <= interx(hull[(int)hull.size()-2].first,hull.back().first))
hull.pop_back();
hull.push_back({cur,dp[u].second});
while((int)hull.size()>1 && hull[0].first.eval(v[i].first+1) >= hull[1].first.eval(v[i].first+1))
hull.pop_front();
dp[i].first = hull[0].first.eval(v[i].first+1) + v[i].first*(v[i].first+2) + coef;
dp[i].second = hull[0].second + 1;
}
return dp[n];
}
long long take_photos(int32_t n, int32_t m, int32_t k, std::vector<int32_t> x, std::vector<int32_t> y)
{
for(int i=0;i<n;i++)
{
if(x[i] < y[i])
swap(x[i],y[i]);
v[i+1] = {x[i],y[i]};
}
sort(v+1,v+1+n);
int cv=INF,newn=0;
for(int i=n;i>0;i--)
{
if(v[i].second < cv)
{
newv[++newn] = v[i];
cv = v[i].second;
}
}
reverse(newv+1,newv+1+newn);
n = newn;
for(int i=1;i<=n;i++)
v[i] = newv[i];
v[0] = {-1,-1};
k = min(k, n);
int st=0,dr=INF,ans=-1;
while(st<=dr)
{
int mij=(st+dr)/2;
pair<int,int> aux = calc(n,k,mij);
if(aux.second >= k)
{
ans = mij;
st = mij+1;
}
else
dr = mij-1;
}
pair<int,int> aux = calc(n,k,ans);
return aux.first - ans*k;
}
