You have two permutations of $$$n$$$ elements, $$$p_1, p_2, \ldots, p_n$$$ and $$$q_1, q_2, \ldots, q_n$$$, and one integer $$$k$$$.
You need to find two integer arrays, $$$a$$$ and $$$b$$$, with the following properties:
The first line of the input contains two integers $$$n$$$ and $$$k$$$: the number of elements and the required number of cool pairs ($$$1 \leq n \leq 300\,000$$$, $$$0 \leq k \leq \frac{n \cdot (n - 1)}{2}$$$).
The second line contains $$$n$$$ space-separated integers: the permutation $$$p_1, p_2, \ldots, p_n$$$.
The third line contains $$$n$$$ space-separated integers: the permutation $$$q_1, q_2, \ldots, q_n$$$.
It is guaranteed that each integer from $$$1$$$ to $$$n$$$ appears exactly once in each permutation.
If there is no such pair of integer arrays that the number of cool pairs is equal to $$$k$$$, print "No" on a single line.
Otherwise, print "Yes" on the first line, and print the arrays $$$a$$$ and $$$b$$$ on the next two lines. Separate array elements by spaces.
5 3
3 5 1 2 4
1 2 3 4 5
Yes
2 3 -1 5 1
-5 -3 -2 -2 0