Please read the statement of the easier version first. It has been copied to the notes.
Willy realizes that he has made a big mess, and the number $$$n$$$ of participants who will make the visit is unknown. The only thing he knows is that $$$1 \leq n \leq k$$$. Help Willy Wonka by computing the number of ways to distribute the $$$k$$$ sweets for every possible value of $$$n$$$. Print the answer modulo $$$10^9 + 7$$$.
The input consists of a single integer $$$k$$$, representing the number of chocolates. It is guaranteed that $$$1 \leq k \leq 10^5$$$.
Print $$$k$$$ integers separated by spaces. The integer $$$1 \leq i \leq k$$$ represents how many ways to distribute $$$k$$$ sweets to $$$i$$$ participants such that everyone receives at least one sweet, modulo $$$10^9 + 7$$$.
1
1
2
1 2
5
1 30 150 240 120
Statement of the easier version:
Willy Wonka, famous for his large chocolate factory, decided to give a gift to the $$$n$$$ lucky people awarded a visit to his factory. He has $$$k$$$ chocolates available, all different from each other. Willy wants to distribute the chocolates among the $$$n$$$ participants, ensuring that everyone receives at least one chocolate.
After a while, he realized that this task was too easy and decided to compute how many ways this can be done. Let the $$$k$$$ distinct chocolates be numbered from $$$1$$$ to $$$k$$$, and the participants from $$$1$$$ to $$$n$$$. Two ways are different if there exists some participant $$$i$$$ who receives a chocolate $$$j$$$ in one of the distributions but not in another for some $$$1 \leq i \leq n$$$ and $$$1 \leq j \leq k$$$. Since the number of ways can be very large, compute the answer modulo $$$10^9 + 7$$$.
