When is the answer $$$-1$$$? When is the answer $$$0$$$? When is the answer $$$1$$$?

Can you do all remaining cases in $$$2$$$ steps?

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https://www.youtube.com/watch?v=j_oe8DA4hhM

If the classroom was one-dimensional, i.e. $$$n = 1$$$, where would the best place for Tina to sit be?

The best place for Tina to sit a grid where $$$n = 1$$$ would be either $$$(1, 1)$$$, or $$$(1, m)$$$.

using namespace std;

void solve() {
    int n, m, k;
    cin >> n >> m;
    vector<int> v;
    for (int i = 0; i < n; ++i)
        for (int j = 0; j < m; ++j)
            v.push_back(max(i, n - i - 1) + max(j, m - j - 1));
    sort(v.begin(), v.end());
    for (int i = 0; i < n * m; ++i) 
        cout << v[i] << " ";
    cout << "\n";
}
  
int main() {
    ios_base::sync_with_stdio(0); cin.tie(0);
    int t;
    cin >> t;
    while (t--)
        solve();
    return 0;
}

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https://www.youtube.com/watch?v=rwSzE-V-2V4

When does a valid assignment not exist?

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https://www.youtube.com/watch?v=0TigYx222pY

After applying operations, all elements in the array will be between $$$1$$$ and $$$A$$$ inclusive, where $$$A$$$ is the maximum element of the initial array.

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https://www.youtube.com/watch?v=VdbUkNgjiy0

Try solving for $$$n, m, k \le 1000$$$.

Do we need to account for all $$$n \cdot m$$$ rooms?

Solve for each row independently.

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What can you say about all valid cuts?

The cuts are rotationally symmetric about the center. How do we find the cut that breaks the fewest edges?

Shortest paths.

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The problem was originally written as problem E, with a harder F, but we decided that the other F was too hard and moved this problem to F.

Sorry for the statement of the problem initially. It was correct throughout testing, but during translation it seems that it might have been changed from subsequence to subarray accidentally.