#include "tickets.h"
#include <vector>
#include <algorithm>
#include <cassert>
using namespace std;
const long long INF = 1e18;
long long find_maximum(int k, vector<vector<int>> x) {
int n = x.size();
int m = x[0].size();
vector<vector<int>> answer(n, vector<int>(m, -1));
long long prize = 0;
int MAX = 0;
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
MAX = max(MAX, x[i][j]);
}
}
if (k == 1) {
vector<vector<long long>> dp(1+n, vector<long long>(1+n/2, -INF));
dp[0][0] = 0;
// dp on prefix and number of positives
vector<vector<bool>> chosePositive(1+n, vector<bool>(1+n/2));
// chosePositive allows backtracking
for (int i = 0; i < n; ++i) {
for (int pos = 0; 2*pos <= n; ++pos) {
if (dp[i][pos] == -INF) continue;
// do not choose positive
long long v = dp[i][pos] - x[i].front();
if (v > dp[i+1][pos]) {
dp[i+1][pos] = v;
chosePositive[i+1][pos] = false;
}
// choose positive (if possible)
if (2*pos == n) continue; // no more positives
v = dp[i][pos] + x[i].back();
if (v > dp[i+1][pos+1]) {
dp[i+1][pos+1] = v;
chosePositive[i+1][pos+1] = true;
}
}
}
prize = dp[n][n>>1];
// Now reconstruct answer
for (int i = n, pos = n>>1; i >= 1; --i) {
if (!chosePositive[i][pos]) answer[i-1][0] = 0;
else answer[i-1][m-1] = 0, pos--;
}
} else if (m == k) {
vector<int> cnt[2], remain[2];
cnt[0].resize(n), cnt[1].resize(n);
remain[0].resize(n), remain[1].resize(n);
vector<pair<int, int>> v;
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) v.emplace_back(x[i][j], i);
}
sort(v.begin(), v.end());
for (int i = 0; (i<<1) < n*m; ++i) {
++cnt[0][v[i].second];
}
for (int i = 0; i < n; ++i) {
cnt[1][i] = m-cnt[0][i];
remain[0][i] = cnt[0][i];
remain[1][i] = cnt[1][i];
}
for (int i = 0; i < k; ++i) {
int used0 = 0;
for (int y = 0; y < n; ++y) {
if (!remain[1][y]) { // zero
prize -= x[y][cnt[0][y]-remain[0][y]];
answer[y][cnt[0][y]-remain[0][y]] = i;
--remain[0][y];
++used0;
} else if (!remain[0][y]) { // one
prize += x[y][cnt[0][y]+remain[1][y]-1];
answer[y][cnt[0][y]+remain[1][y]-1] = i;
--remain[1][y];
}
}
for (int y = 0; y < n; ++y) { // both
if (!remain[0][y] || !remain[1][y]) continue;
if (2*used0 < n) {
prize -= x[y][cnt[0][y]-remain[0][y]];
answer[y][cnt[0][y]-remain[0][y]] = i;
--remain[0][y];
++used0;
} else {
prize += x[y][cnt[0][y]+remain[1][y]-1];
answer[y][cnt[0][y]+remain[1][y]-1] = i;
--remain[1][y];
}
}
}
} else if (MAX == 1) {
int z = 0, o = 0;
vector<int> got0(n), got1(n);
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
if (x[i][j] == 0) ++z, ++got0[i];
else ++o, ++got1[i];
}
}
// have to remove (m-k)*n
int zTarget = 0, rem = (m-k)*n;
zTarget = (rem+(z-o))/2;
int mnRemove = 0, mxRemove = 0; // zeros removed
vector<int> mn(1+n), mx(1+n);
for (int i = 0; i < n; ++i) {
mnRemove += max(m-k-got1[i], 0);
mxRemove += min(m-k, got0[i]);
mn[i+1] = mnRemove;
mx[i+1] = mxRemove;
}
// Recalculate realistic target
if (zTarget < mnRemove) zTarget = mnRemove;
if (zTarget > mxRemove) zTarget = mxRemove;
// Remove so that target is achieved
vector<int> removed0(n), removed1(n);
for (int i = n; i >= 1; --i) {
int least = max(m-k-got1[i-1], 0);
int most = min(m-k, got0[i-1]);
int largestAfter = mx[i-1];
removed0[i-1] = max(zTarget-largestAfter, least);
assert(least <= removed0[i-1] && removed0[i-1] <= most);
removed1[i-1] = m-k-removed0[i-1];
zTarget -= removed0[i-1];
}
// This is the same as the solution to m=k except one detail below
vector<int> cnt[2], remain[2];
cnt[0].resize(n), cnt[1].resize(n);
remain[0].resize(n), remain[1].resize(n);
vector<pair<int, int>> v;
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) v.emplace_back(x[i][j], i);
}
sort(v.begin(), v.end());
for (int i = 0; (i<<1) < n*m; ++i) {
++cnt[0][v[i].second];
}
for (int i = 0; i < n; ++i) {
cnt[1][i] = m-cnt[0][i];
remain[0][i] = cnt[0][i];
remain[1][i] = cnt[1][i];
// Here we are subtracting removed from remain
remain[0][i] -= removed0[i];
remain[1][i] -= removed1[i];
assert(remain[0][i] >= 0 && remain[0][i] <= cnt[0][i]);
assert(remain[1][i] >= 0 && remain[1][i] <= cnt[1][i]);
}
for (int i = 0; i < k; ++i) {
int used0 = 0;
for (int y = 0; y < n; ++y) {
if (!remain[1][y]) { // zero
prize -= x[y][cnt[0][y]-remain[0][y]];
answer[y][cnt[0][y]-remain[0][y]] = i;
--remain[0][y];
++used0;
} else if (!remain[0][y]) { // one
prize += x[y][cnt[0][y]+remain[1][y]-1];
answer[y][cnt[0][y]+remain[1][y]-1] = i;
--remain[1][y];
}
}
for (int y = 0; y < n; ++y) { // both
if (!remain[0][y] || !remain[1][y]) continue;
if (2*used0 < n) {
prize -= x[y][cnt[0][y]-remain[0][y]];
answer[y][cnt[0][y]-remain[0][y]] = i;
--remain[0][y];
++used0;
} else {
prize += x[y][cnt[0][y]+remain[1][y]-1];
answer[y][cnt[0][y]+remain[1][y]-1] = i;
--remain[1][y];
}
}
}
}
allocate_tickets(answer);
return prize;
}
