#include <bits/stdc++.h>
using namespace std;
//#define int long long
#define ff first
#define ss second
#define pii pair<int, int>
#define all(x) x.begin(), x.end()
#define rep(i, a, b) for (int i = (int)a; i <= (int)b; ++i)
#define rep1(i, a, b) for (int i = (int)a; i >= (int)b; --i)
#define mp make_pair
#define vii vector<vector<int>>
#define ll long long
void allocate_tickets(vii a);
struct ticket{
int color, order, value;
};
bool operator < (const ticket &x, const ticket &y) {
if (x.value == y.value) {
return mp(x.color, x.order) < mp(y.color, y.order);
}
return x.value < y.value;
}
ll find_maximum(int k, vii a) {
int n = a.size(), m = a[0].size();
vii allo(n, vector<int> (m));
ll prize = 0;
vector<ticket> Replace;
vector<int> Plus(n + 1, k);
rep(i, 0, n - 1) {
rep1(j, m - 1, m - k) {
prize += a[i][j];
allo[i][j] = 1;
}
rep(j, 0, k - 1) {
ticket tmp;
tmp.color = i;
tmp.order = j;
tmp.value = a[i][j] + a[i][m - k + j];
Replace.push_back(tmp);
}
}
sort(all(Replace));
rep(i, 1, k * (n / 2)) {
auto [color, order, value] = Replace[i - 1];
prize -= value;
--Plus[color];
allo[color][m - k + order] = 0;
allo[color][order] = -1;
}
vector<int> v(n);
rep(i, 0, n - 1) v[i] = i;
sort(all(v), [&](int x, int y) {
return Plus[x] < Plus[y];
});
int start = -1;
rep(ii, 0, n - 1) {
int i = v[ii];
vector<bool> used(m);
rep(j, 0, m - 1) {
if (allo[i][j] != -1) break;
start = (start + 1) % k;
allo[i][j] = start + 1;
used[start] = 1;
}
int fin = 0;
rep1(j, m - 1, 0) {
if (allo[i][j] != 1) break;
while (fin < k && used[fin]) ++ fin;
if (fin >= k) break;
allo[i][j] = fin + 1;
++fin;
}
}
rep(i, 0, n - 1) rep(j, 0, m - 1) --allo[i][j];
allocate_tickets(allo);
return prize;
}
