An unordered pair of natural numbers is called good if one of the numbers divides the other. Output $$$n$$$ such natural numbers not exceeding one million, such that there are exactly $$$k$$$ good pairs among them, or determine that this is impossible.
More formally: for the numbers output by your program $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$, there must be exactly $$$k$$$ pairs of indices $$$i$$$, $$$j$$$, where $$$i \lt j$$$, such that $$$a_i$$$ divides $$$a_j$$$ or $$$a_j$$$ divides $$$a_i$$$.
Two integers $$$n$$$ and $$$k$$$ are given, each on a separate line ($$$1 \le n \le 10^5$$$, $$$0 \le k \le 10^5$$$).
Output $$$n$$$ such natural numbers in the range from 1 to $$$10^{6}$$$, such that there are exactly $$$k$$$ good pairs among them. If there are multiple correct answers, output any. If there are no solutions, output -1.
Subtask 1 (up to 30 points): $$$n \le 5$$$.
Subtask 2 (up to 30 points): $$$n \le 100$$$.
Subtask 3 (up to 40 points): no additional constraints.
43
2 2 4 7
2100
-1
