A14192. 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:

- $[1,2,3]$ ,
- $[3,1,2]$ ,
- $[2,3,1]$ .