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Minimum Reverse Operations

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 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:

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

Minimum Reverse Operations diagram

Example 1

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

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

Example 2

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

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

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 <= 10^5
  • 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

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