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 Format: 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 Format: 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 $$$10^9+7$$$. 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: - $$$[1,2,3]$$$, - $$$[3,1,2]$$$, - $$$[2,3,1]$$$.