It is an interactive problem.

We have an array $$$a$$$ that we don't know (**and cannot modify**) and we are given an array $$$b$$$ of the same size as $$$a$$$. (length of $$$a$$$ is less then $$$4\ 000$$$).

We need to arange the elements in the array $$$b$$$ such that the cross product of arrays $$$a$$$ and $$$b$$$ is maximal. ($$$a_1 * b_1 + ... + a_n * b_n$$$ is maximal).

The interaction consist in giving the arary $$$b$$$ and reciveing the corss product with $$$a$$$ every time. How can we find a rearangement of array $$$b$$$ such that