Mr. L is the owner of a company with $$$n$$$ employees and $$$n$$$ positions. The $$$i$$$-th employee has a capability value of $$$a_i$$$, and the $$$j$$$-th position has a requirement value of $$$b_j$$$. The base profit generated when the $$$i$$$-th employee is assigned to the $$$j$$$-th position is: $$$a_i + b_j + (a_i \oplus b_j)$$$, where $$$\oplus$$$ denotes the XOR operation in binary.
Additionally, Mr. L discovered that specific employee-position assignments yield extra profits. He provides $$$m$$$ pieces of information in the form $$$(x, y, w)$$$, indicating that assigning the $$$x$$$-th employee to the $$$y$$$-th position results in an additional profit of $$$w$$$.
Given a parameter $$$K$$$, Mr. L wants to determine, for each $$$1 \leq k \leq K$$$, the maximum total profit (base profit + additional profit) achievable when exactly $$$k$$$ employees are assigned to positions.
Note: Two employees cannot be assigned to the same position.
The first line contains three integers $$$n,m,K$$$ ($$$1 \leq n \leq 10^5,0 \leq m \leq 5 \times 10^5,1 \le K \le \min(300,n)$$$), denoting the number of employees/positions, the number of information entries, and the given parameter.
The second line contains $$$n$$$ integers, where the $$$i$$$-th integer denotes $$$a_i$$$ ($$$0 \leq a_i \lt 2^{12}$$$).
The third line contains $$$n$$$ integers, where the $$$i$$$-th integer denotes $$$b_i$$$ ($$$0 \leq b_i \lt 2^{12}$$$).
The next $$$m$$$ lines each contain three integers $$$x$$$, $$$y$$$, and $$$w$$$ ($$$1 \leq x \leq n$$$, $$$1 \leq y \leq n$$$, $$$0 \leq w \leq 10^5$$$).
It is guaranteed that no two pieces of information share identical $$$x$$$ and $$$y$$$ values.
Output a single line containing $$$K$$$ integers, where the $$$i$$$-th integer denotes the answer when $$$k = i$$$.
5 0 51 2 3 4 55 4 3 2 1
14 28 42 56 58
