/*
Author of all code: Pedro BIGMAN Dias
Last edit: 15/02/2021
*/
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")
#pragma GCC optimize("Ofast")
#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <string>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <queue>
#include <deque>
#include <list>
#include <iomanip>
#include <stdlib.h>
#include <time.h>
#include <cstring>
#include "tickets.h"
using namespace std;
typedef long long int ll;
typedef unsigned long long int ull;
typedef long double ld;
#define REP(i,a,b) for(ll i=(ll) a; i<(ll) b; i++)
#define pb push_back
#define mp make_pair
#define pl pair<ll,ll>
#define ff first
#define ss second
#define whole(x) x.begin(),x.end()
#define DEBUG(i) cout<<"Pedro Is The Master "<<i<<endl
#define INF 1000000000000000000LL
#define EPS ((ld)0.00000000001)
#define pi ((ld)3.141592653589793)
#define VV(vvvv,NNNN,xxxx); REP(iiiii,0,NNNN) {vvvv.pb(xxxx);}
ll mod=1000000007LL;
template<class A=ll>
void Out(vector<A> a) {REP(i,0,a.size()) {cout<<a[i]<<" ";} cout<<endl;}
template<class A=ll>
void In(vector<A> &a, ll N) {A cur; REP(i,0,N) {cin>>cur; a.pb(cur);}}
ll Value(vector<vector<ll> > ans, vector<vector<int> > X)
{
ll val=0LL;
REP(i,0,X.size()) {REP(j,0,X[i].size()) {val+=((ll) (ans[i][j]*X[i][j]));}}
return val;
}
vector<vector<int> > Order(vector<vector<ll> > ans, ll K)
{
ll N = ans.size(); ll M = ans[0].size();
vector<vector<int> > a; vector<int> xx; VV(xx,M,-1); VV(a,N,xx);
vector<pl> ones; REP(i,0,N) {ll cursum=0; REP(j,0,M) {cursum+=ans[i][j];} ones.pb({cursum,i});}
sort(whole(ones));
vector<ll> indleft,indright; VV(indleft,N,0); VV(indright,N,M-1); ll ind;
REP(i,0,K)
{
vector<pl> newones;
REP(j,0,N/2) {ind = ones[j].ss; newones.pb({ones[j].ff+1,ind}); a[ind][indleft[ind]]=i; indleft[ind]++;}
REP(j,N/2,N) {ind = ones[j].ss; newones.pb({ones[j].ff-1,ind}); a[ind][indright[ind]]=i; indright[ind]--;}
sort(whole(newones)); ones=newones;
}
return a;
}
ll find_maximum(int k, vector<vector<int> > x)
{
ll N = x.size(); ll M = x[0].size(); ll K = (ll) k;
vector<vector<ll> > ans; vector<ll> xx; VV(xx,M,0); VV(ans,N,xx);
if(M==K)
{
vector<pair<ll,pl> > vals; REP(i,0,N) {REP(j,0,M) {vals.pb({x[i][j],{i,j}});}}
sort(whole(vals)); REP(i,0,(N*M)/2) {ans[vals[i].ss.ff][vals[i].ss.ss]=-1;} REP(i,(N*M)/2,N*M) {ans[vals[i].ss.ff][vals[i].ss.ss]=1;}
}
else
{
set<pl> small,big; vector<ll> ind; VV(ind,N/2,0); VV(ind,N/2,K); set<pl>::iterator it;
REP(i,0,N)
{
ll val_small; if(ind[i]==0) {val_small=-INF;} else {val_small=x[i][ind[i]-1]+x[i][ind[i]+M-K-1];}
ll val_big; if(ind[i]==K) {val_big=INF;} else {val_big=x[i][ind[i]]+x[i][ind[i]+M-K];}
small.insert({val_small,i}); big.insert({val_big,i});
}
while(1>0)
{
it=small.end(); it--; pl max_small = *it; small.erase(it);
it=big.begin(); pl min_big = *it; big.erase(it);
if(max_small.ff<=min_big.ff) {break;}
ll ind_small = max_small.ss; ll ind_big = min_big.ss;
ind[ind_small]--; ind[ind_big]++;
ll val_small,val_big;
ll i=ind_small;
if(ind[i]==0) {val_small=-INF;} else {val_small=x[i][ind[i]-1]+x[i][ind[i]+M-K-1];}
if(ind[i]==K) {val_big=INF;} else {val_big=x[i][ind[i]]+x[i][ind[i]+M-K];}
small.insert({val_small,i}); big.insert({val_big,i});
i=ind_big;
if(ind[i]==0) {val_small=-INF;} else {val_small=x[i][ind[i]-1]+x[i][ind[i]+M-K-1];}
if(ind[i]==K) {val_big=INF;} else {val_big=x[i][ind[i]]+x[i][ind[i]+M-K];}
small.insert({val_small,i}); big.insert({val_big,i});
}
REP(i,0,N) {REP(j,0,ind[i]) {ans[i][j]=-1;} REP(j,ind[i]+M-K,M) {ans[i][j]=1;}}
}
allocate_tickets(Order(ans,K));
return Value(ans,x);
}
