[Solution] Not Sitting solution codeforces – Rahul and Tina are aware of each other’s intentions and they both choose seats as strategically as possible? Please help satisfy Rahul’s curiosity!

Not Sitting solution codeforces

Not Sitting solution codeforces – Rahul and Tina are looking forward to starting their new year at college. As they enter their new classroom, they observe the seats of students are arranged in a n×mn×m grid. The seat in row rr and column cc is denoted by (r,c)(r,c), and the distance between two seats (a,b)(a,b) and (c,d)(c,d) is |ac|+|bd||a−c|+|b−d|.

As the class president, Tina has access to exactly kk buckets of pink paint. The following process occurs.

  • First, Tina chooses exactly kk seats in the classroom to paint with pink paint. One bucket of paint can paint exactly one seat.
  • After Tina has painted kk seats in the previous step, Rahul chooses where he sits. He will not choose a seat that has been painted pink due to his hatred of the colour pink.
  • After Rahul has chosen his seat, Tina chooses a seat for herself. She can choose any of the seats, painted or not, other than the one chosen by Rahul.

Rahul wants to choose a seat such that he sits as close to Tina as possible. However, Tina wants to sit as far away from Rahul as possible due to some complicated relationship history that we couldn’t fit into the statement!

Now, Rahul wonders for k=0,1,,nm1k=0,1,…,n⋅m−1, if Tina has kk buckets of paint, how close can Rahul sit to Tina, if both Rahul and Tina are aware of each other’s intentions and they both choose seats as strategically as possible? Please help satisfy Rahul’s curiosity!

Not Sitting solution codeforces Input

The input consists of multiple test cases. The first line contains an integer tt (1t51041≤t≤5⋅104) — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers nnmm (2nm1052≤n⋅m≤105) — the number of rows and columns of seats in the classroom.

The sum of nmn⋅m across all test cases does not exceed 105105.

Output Not Sitting solution codeforces

For each test case, output nmn⋅m ordered integers — the distance between Rahul and Tina if both of them choose their seats optimally for every k[0,nm1]k∈[0,n⋅m−1].

Example
input

Copy
2
4 3
1 2
output

Copy
3 3 4 4 4 4 4 4 5 5 5 5 
1 1 

Not Sitting solution codeforces Note

One possible sequence of choices for the first testcase where Tina has k=3k=3 buckets of paints is as follows.

Tina paints the seats at positions (1,2)(1,2)(2,2)(2,2)(3,2)(3,2) with pink paint. Rahul chooses the seat at (3,1)(3,1) after which Tina chooses to sit at (1,3)(1,3).

Therefore, the distance between Tina and Rahul is |31|+|13|=4|3−1|+|1−3|=4, and we can prove that this is indeed the minimum possible distance under the given constraints. There may be other choices of seats which lead to the same answer as well.

For k=0k=0 in the first test case, Rahul can decide to sit at (2,2)(2,2) and Tina can decide to sit at (4,3)(4,3) so the distance between them would be |24|+|23|=3|2−4|+|2−3|=3.

Below are pictorial representations of the k=3k=3 and k=0k=0 cases for the first test case.

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