#include "tickets.h"
#include <bits/stdc++.h>
using namespace std;
long long report(int n, int m, int k, vector<vector<int>>& x, vector<int>& c){
vector<vector<int>> ans(n, vector<int>(m, -1));
vector<pair<int, int>> v;
for(int i = 0; i < n; i++){
v.push_back({c[i], i});
}
vector<int> l(n, 0), r(n, m - 1);
long long res = 0;
for(int i = 0; i < k; i++){
sort(v.begin(), v.end(), [](pair<int, int> p1, pair<int, int> p2){
return p1.first > p2.first;
});
for(int j = 0; j < n / 2; j++){
res += x[v[j].second][r[v[j].second]];
ans[v[j].second][r[v[j].second]--] = i;
v[j].first--;
}
for(int j = n / 2; j < n; j++){
res -= x[v[j].second][l[v[j].second]];
ans[v[j].second][l[v[j].second]++] = i;
}
}
allocate_tickets(ans);
return res;
}
struct value_key{
long long value, key, id; bool negative;
bool operator< (const value_key& o) const {
return value < o.value;
}
};
struct result_type{
int left, right;
};
bool used[1500 * 1500];
result_type lambda_maximum(long long lambda, int n, int m, int k, vector<value_key>& a, vector<int>& p, vector<int>& p2){
int L = 0, R = n * m - 1;
fill(used, used + n * m, false);
vector<long long> cnt(n, 0), prev_value(n, -(1LL << 31)), prev_cnt(n, 0);
fill(p.begin(), p.end(), 0);
fill(p2.begin(), p2.end(), 0);
int left_bound = 0, right_bound = 0;
while(L < n * m || R >= 0){
long long value; int key, id; bool negative;
if(R == -1 || (L < n * m && lambda - a[L].value >= a[R].value)){
value = lambda - a[L].value; key = a[L].key; id = a[L++].id; negative = true;
}else{
value = a[R].value; key = a[R].key; id = a[R--].id; negative = false;
}
if(used[id]){
if(value * 2 == lambda){
if(negative){
p[key]--; p2[key]++; left_bound--;
}else{
p2[key]++; right_bound++;
}
}
continue;
}
if(cnt[key] < k){
used[id] = true;
cnt[key]++; if(!negative) p[key]++, left_bound++, right_bound++;
prev_cnt[key] = (prev_value[key] == value ? prev_cnt[key] + (negative) : negative);
prev_value[key] = value;
}else if(prev_value[key] == value){
if(!negative && prev_cnt[key] > 0) prev_cnt[key]--, p2[key]++, right_bound++;
}
}
return {left_bound, right_bound};
}
long long find_maximum(int k, vector<vector<int>> x) {
int n = x.size(), m = x[0].size();
for(int i = 0; i < n; i++){
for(int j = 0; j < m; j++){
x[i][j] <<= 1;
}
}
vector<value_key> a;
for(int i = 0; i < n; i++){
for(int j = 0; j < m; j++){
a.push_back({x[i][j], i, i * m + j});
}
}
sort(a.begin(), a.end());
long long L = 0, R = 1LL << 32;
vector<int> p(n), p2(n);
while(L <= R){
long long M = (L + R) / 2;
result_type range = lambda_maximum(M, n, m, k, a, p, p2);
if(range.right < n * k / 2){
R = M - 1;
}else if(range.left > n * k / 2){
L = M + 1;
}else{
int cnt = range.left;
for(int i = 0; i < n; i++){
while(cnt < n * k / 2 && p2[i] > 0){
cnt++; p[i]++; p2[i]--;
}
}
long long ans = report(n, m, k, x, p) >> 1;
return ans;
}
}
return -1;
}
