F. Covering Circletime limit per test6 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputSam started playing with round buckets in the sandbox, while also scattering pebbles. His mom decided to buy him a new bucket, so she needs to solve the following task.You are given n distinct points with integer coordinates A_1, A_2, \ldots, A_n. All points were generated from the square [-10^8, 10^8] \times [-10^8, 10^8] uniformly and independently.You are given positive integers k, l, such that k \leq l \leq n. You want to select a subsegment A_i, A_{i+1}, \ldots, A_{i+l-1} of the points array (for some 1 \leq i \leq n + 1 - l), and some circle on the plane, containing \geq k points of the selected subsegment (inside or on the border).What is the smallest possible radius of that circle?InputEach test contains multiple test cases. The first line contains a single integer t (1 \leq t \leq 10^4) — the number of test cases. Descriptions of test cases follow.The first line of each test case contains three integers n, l, k (2 \leq k \leq l \leq n \leq 50\,000, k \leq 20).Each of the next n lines contains two integers x_i, y_i (-10^8 \leq x_i, y_i \leq 10^8) — the coordinates of the point A_i. It is guaranteed that all points are distinct and were generated independently from uniform distribution on [-10^8, 10^8] \times [-10^8, 10^8].It is guaranteed that the sum of n for all test cases does not exceed 50\,000.In the first test, points were not generated from the uniform distribution on [-10^8, 10^8] \times [-10^8, 10^8] for simplicity. It is the only such test and your solution must pass it.Hacks are disabled in this problem.OutputFor each test case print a single real number — the answer to the problem.Your answer will be considered correct if its absolute or relative error does not exceed 10^{-9}. Formally let your answer be a, jury answer be b. Your answer will be considered correct if \frac{|a - b|}{\max{(1, |b|)}} \le 10^{-9}.ExampleInput
4
3 2 2
0 0
0 4
3 0
5 4 3
1 1
0 0
2 2
0 2
2 0
8 3 2
0 3
1 0
0 2
1 1
0 1
1 2
0 0
1 3
5 4 4
1 1
-3 3
2 2
5 3
5 5
Output
2.00000000000000000000
1.00000000000000000000
0.50000000000000000000
4.00000000000000000000
NoteIn the first test case, we can select subsegment A_1, A_2 and a circle with center (0, 2) and radius 2.In the second test case, we can select subsegment A_1, A_2, A_3, A_4 and a circle with center (1, 2) and radius 1.
4
3 2 2
0 0
0 4
3 0
5 4 3
1 1
0 0
2 2
0 2
2 0
8 3 2
0 3
1 0
0 2
1 1
0 1
1 2
0 0
1 3
5 4 4
1 1
-3 3
2 2
5 3
5 5

2.00000000000000000000 1.00000000000000000000 0.50000000000000000000 4.00000000000000000000 
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