Editorial for Meeting Table

Step 1: First group can be sitted in (N1)!\textbf (N-1)! different ways. (Why?)

Step 2: Second group of people can be sitted in N!\textbf N! different ways to maintain the given constraint.

Step 3: Third group can choose spaces between the previous groups (2NN)2N \choose N to sit and maintain the constraint. They can arrange themselves in N!\textbf N! ways.

You will need to precalculate the (N!mod109+7)(N! \mod 10^{9}+7) and (1N!mod109+7)(\frac{1}{N!} \mod 10^{9}+7) for all 1<=N<=1071<=N<=10^{7}. Try to precalculate the inverse modulo part in O(N).

Time Complexity: O( T + MAXN) Where MAXN = 10710^7

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