CF1516E Baby Ehab Plays with Permutations

This time around, Baby Ehab will play with permutations. He has $ n $ cubes arranged in a row, with numbers from $ 1 $ to $ n $ written on them. He'll make exactly $ j $ operations. In each operation, he'll pick up $ 2 $ cubes and switch their positions. He's wondering: how many different sequences of cubes can I have at the end? Since Baby Ehab is a turbulent person, he doesn't know how many operations he'll make, so he wants the answer for every possible $ j $ between $ 1 $ and $ k $ .

The only line contains $ 2 $ integers $ n $ and $ k $ ( $ 2 \le n \le 10^9 $ , $ 1 \le k \le 200 $ ) — the number of cubes Baby Ehab has, and the parameter $ k $ from the statement.

Print $ k $ space-separated integers. The $ i $ -th of them is the number of possible sequences you can end up with if you do exactly $ i $ operations. Since this number can be very large, print the remainder when it's divided by $ 10^9+7 $ .

In the second example, there are $ 3 $ sequences he can get after $ 1 $ swap, because there are $ 3 $ pairs of cubes he can swap. Also, there are $ 3 $ sequences he can get after $ 2 $ swaps: - $ [1,2,3] $ , - $ [3,1,2] $ , - $ [2,3,1] $ .