For this problem, we must construct a permutation ~b~, by using integers from ~1~ to ~N~ such that the number of unique integers obtained from calculating the GCD of the element at the ~i^{th}~ position and the element at the ~a_i^{th}~ position of array ~a~ is exactly ~K~.

There are many different strategies to construct such an array, and one of the possible solutions will be discussed in this editorial.

Subtask 1

If ~K = 1~, we can create an array ~a~ by set ~a_i = i + 1~ for all ~i~ where ~1 \leq i \leq N - 1~, and ~a_N = 1~.
If ~K = N~, we can create an array ~a~ by set ~a_i = i~ for all ~i~ where ~1 \leq i \leq N~.

Subtask 2

We can split the creation of the array into two separate loops, one covering positions from ~1~ to ~N-K+1~, and the other covering positions from ~N-K+2~ to ~N~.

The implementation details are left as an exercise for the reader.

Time Complexity: ~\mathcal{O}(N)~