You are given an integer n and an integer p representing an array arr of length n where all elements are set to 0's, except position p which is set to 1. You are also given an integer array banned containing restricted positions. Perform the following operation on arr:

Reverse a subarray with size k if the single 1 is not set to a position in banned.

Return an integer array answer with n results where the i^th result is the minimum number of operations needed to bring the single 1 to position i in arr, or -1 if it is impossible.

Example 1:

Input: n = 4, p = 0, banned = [1,2], k = 4

Output: [0,-1,-1,1]

Explanation:

Initially 1 is placed at position 0 so the number of operations we need for position 0 is 0.
We can never place 1 on the banned positions, so the answer for positions 1 and 2 is -1.
Perform the operation of size 4 to reverse the whole array.
After a single operation 1 is at position 3 so the answer for position 3 is 1.

Example 2:

Input: n = 5, p = 0, banned = [2,4], k = 3

Output: [0,-1,-1,-1,-1]

Explanation:

Initially 1 is placed at position 0 so the number of operations we need for position 0 is 0.
We cannot perform the operation on the subarray positions [0, 2] because position 2 is in banned.
Because 1 cannot be set at position 2, it is impossible to set 1 at other positions in more operations.

Example 3:

Input: n = 4, p = 2, banned = [0,1,3], k = 1

Output: [-1,-1,0,-1]

Explanation:

Perform operations of size 1 and 1 never changes its position.

Constraints:

1 <= n <= 10⁵
0 <= p <= n - 1
0 <= banned.length <= n - 1
0 <= banned[i] <= n - 1
1 <= k <= n
banned[i] != p
all values in banned are unique