Baby Ehab Plays with Permutations

2000ms

262144K

Description:

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 $$$k$$$.

Input:

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.

Output:

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 $$$10^9+7$$$.

Sample Input:

2 3

Sample Output:

1 1 1

Sample Input:

3 2

Sample Output:

3 3

Sample Input:

4 2

Sample Output:

6 12

Note:

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:

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

Informação

Provedor Codeforces

Código CF1516E