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Red Zone

Problem Description

There are many people who believe that the earth is flat and NASA is a scam. They call themselves Flat Earthers. They were already worried that the 6 feet social distancing rule might push some people out of the earth.

Now, they decided to think about a new issue. Since the earth is flat ( or so they think), let's imagine it as an infinite 2D grid. They have the coordinates of certain points which are orange zones and have some COVID-19 cases reported. Now each day the orange zones become more fatal. After d days, all the locations within a euclidean distance of d of a particular orange zone can be affected by this zone.

They know N orange zones, each of whose coordinates are given by (A[i][0], A[i][1]). Now, a location is considered a red zone if it is affected by at least B orange zones. You need to find the first day at which the first red zone is reported.



Problem Constraints

2 <= B <= N <= 100

0 <= A[i][0], A[i][1] <= 109



Input Format

The first argument contains a 2D array A of size N, denoting the coordinates of the orange zones.

The second argument contains an integer B.



Output Format

Return the first day at which the first red zone is reported.



Example Input

Input 1:

  A : 
  [
    [8, 5]
    [0, 4]
    [3, 6]
  ]
  B : 3

Input 2:

  A : 
  [
    [2, 3]
    [9, 4]
    [10, 3]
  ]
  B : 2



Example Output

Output 1:

  5

Output 2:

  1



Example Explanation

Explanation 1:

  One of the red zones will be (5, 4) and it is within a distance of 5 from all the orange zones.

Explanation 2:

  One of the red zones will be (9, 3) and it is within a distance of 1 from 2 orange zones.



NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
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