There is an infinite 2D plane.

You are given a positive integer k. You are also given a 2D array queries, which contains the following queries:

After each query, you need to find the distance of the kth nearest obstacle from the origin.

Return an integer array results where results[i] denotes the kth nearest obstacle after query i, or results[i] == -1 if there are less than k obstacles.

Note that initially there are no obstacles anywhere.

The distance of an obstacle at coordinate (x, y) from the origin is given by |x| + |y|.

 

Example 1:

Input: queries = [[1,2],[3,4],[2,3],[-3,0]], k = 2

Output: [-1,7,5,3]

Explanation:

Example 2:

Input: queries = [[5,5],[4,4],[3,3]], k = 1

Output: [10,8,6]

Explanation:

 

Constraints: