You are given a code contest problem:

problem name: '1575_B. Building an Amusement Park'


problem description:
=====
Mr. Chanek lives in a city represented as a plane. He wants to build an amusement park in the shape of a circle of radius r. The circle must touch the origin (point (0, 0)).

There are n bird habitats that can be a photo spot for the tourists in the park. The i-th bird habitat is at point p_i = (x_i, y_i). 

Find the minimum radius r of a park with at least k bird habitats inside. 

A point is considered to be inside the park if and only if the distance between p_i and the center of the park is less than or equal to the radius of the park. Note that the center and the radius of the park do not need to be integers.

In this problem, it is guaranteed that the given input always has a solution with r ≤ 2 ⋅ 10^5.

Input

The first line contains two integers n and k (1 ≤ n ≤ 10^5, 1 ≤ k ≤ n) — the number of bird habitats in the city and the number of bird habitats required to be inside the park.

The i-th of the next n lines contains two integers x_i and y_i (0 ≤ |x_i|, |y_i| ≤ 10^5) — the position of the i-th bird habitat.

Output

Output a single real number r denoting the minimum radius of a park with at least k bird habitats inside. It is guaranteed that the given input always has a solution with r ≤ 2 ⋅ 10^5.

Your answer is considered correct if its absolute or relative error does not exceed 10^{-4}.

Formally, let your answer be a, and the jury's answer be b. Your answer is accepted if and only if \frac{|a - b|}{max{(1, |b|)}} ≤ 10^{-4}.

Examples

Input


8 4
-3 1
-4 4
1 5
2 2
2 -2
-2 -4
-1 -1
-6 0


Output


3.1622776589


Input


1 1
0 0


Output


0.0000000000

Note

In the first example, Mr. Chanek can put the center of the park at (-3, -1) with radius √{10} ≈ 3.162. It can be proven this is the minimum r.

The following illustrates the first example. The blue points represent bird habitats and the red circle represents the amusement park.

<image>
=====


Given the code contest problem, you have two tasks:
1) Reflect on the problem, and describe it in your own words, in bullet points. Pay attention to small details, nuances, notes and examples in the problem description.
2) Explain how each provided example input leads to the corresponding output (in total 2 examples are provided).
Read carefully the problem description. Make sure the test explanations are consistent with them, and between themselves.
The explanation must coherently and logically lead from the input to the output. Be as specific as possible.

The output must be a YAML object equivalent to type $ProblemReflection, according to the following Pydantic definitions:
=====
Class InputOutput(BaseModel):
    input: str
    output: str
    explanation: str = Field(description="Short explanation how the test input leads to the test output.")


class ProblemReflection(BaseModel):
    self_reflection: str = Field(description="Describe the problem in your own words, in bullet points. Address the problem goals, inputs, outputs, rules, constraints, and other relevant details.")
    tests_explanations: list[InputOutput] = Field(max_items=2, description="List of explanations for each test case")
=====

Example YAML output:
```yaml
self_reflection:
- |
  ...
- |
  ...
tests_explanations:
- input: |
    ...
  output: |
    ..
  explanation: |
    ...
...
 ```