Problem:
Score : 600 points

Problem Statement

Takahashi wants to grill N pieces of meat on a grilling net, which can be seen as a two-dimensional plane. The coordinates of the i-th piece of meat are \left(x_i, y_i\right), and its hardness is c_i.

Takahashi can use one heat source to grill the meat. If he puts the heat source at coordinates \left(X, Y\right), where X and Y are real numbers, the i-th piece of meat will be ready to eat in c_i \times \sqrt{\left(X - x_i\right)^2 + \left(Y-y_i\right)^2} seconds.

Takahashi wants to eat K pieces of meat. Find the time required to have K or more pieces of meat ready if he put the heat source to minimize this time.

Constraints

All values in input are integers.

1 \leq N \leq 60

1 \leq K \leq N

-1000 \leq x_i , y_i \leq 1000

\left(x_i, y_i\right) \neq \left(x_j, y_j\right) \left(i \neq j \right)

1 \leq c_i \leq 100

Input

Input is given from Standard Input in the following format:

N K
x_1 y_1 c_1
\vdots
x_N y_N c_N

Output

Print the answer.

It will be considered correct if its absolute or relative error from our answer is at most 10^{-6}.

Sample Input 1

4 3
-1 0 3
0 0 3
1 0 2
1 1 40

Sample Output 1

2.4

If we put the heat source at \left(-0.2, 0\right), the 1-st, 2-nd, and 3-rd pieces of meat will be ready to eat within 2.4 seconds. This is the optimal place to put the heat source.

Sample Input 2

10 5
-879 981 26
890 -406 81
512 859 97
362 -955 25
128 553 17
-885 763 2
449 310 57
-656 -204 11
-270 76 40
184 170 16

Sample Output 2

7411.2252

Solution in PyPy3 (2.4.0) (judge verdict: Accepted)

# -*- coding: utf-8 -*-
import bisect
import heapq
import math
import random
import sys
from collections import Counter, defaultdict, deque
from decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal
from functools import lru_cache, reduce
from itertools import combinations, combinations_with_replacement, product, permutations
from operator import add, mul, sub

sys.setrecursionlimit(100000)
input = sys.stdin.readline
INF = 2**62-1
EPS = 1.0e-8

def read_int():
    return int(input())


def read_int_n():
    return list(map(int, input().split()))


def read_float():
    return float(input())


def read_float_n():
    return list(map(float, input().split()))


def read_str():
    return input().strip()


def read_str_n():
    return list(map(str, input().split()))


def error_print(*args):
    print(*args, file=sys.stderr)


def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap


class Circle:
    def __init__(self, x, y, r):
        self.x = x
        self.y = y
        self.r = r

    def center(self):
        return Point(self.x, self.y)

    def intersection(self, c):
        d = self.center().distance(c.center())
        if d > self.r + c.r:
            return None
        # One circle within other
        if d < abs(self.r - c.r):
            return None
        # coincident circles
        if d == 0 and self.r == c.r:
            return None
        else:
            a = (self.r**2 - c.r**2 + d**2) / (2*d)
            h = math.sqrt(self.r**2-a**2 + sys.float_info.epsilon)
            x2 = self.x+a*(c.x-self.x)/d
            y2 = self.y+a*(c.y-self.y)/d
            x3 = x2+h*(c.y-self.y)/d
            y3 = y2-h*(c.x-self.x)/d

            x4 = x2-h*(c.y-self.y)/d
            y4 = y2+h*(c.x-self.x)/d

            return Point(x3, y3), Point(x4, y4)

class Point:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def distance(self, p):
        return math.sqrt((self.x - p.x)**2 + (self.y - p.y)**2)

class Bisect:
    def __init__(self, func):
        self.__func = func


    def bisect_left(self, x, lo, hi):
        while hi - lo > EPS:
            mid = (lo+hi)/2
            if self.__func(mid) < x:
                lo = mid
            else:
                hi = mid
        return lo

@mt
def slv(N, K, XYC):
    def f(t):
        cs = []
        for x, y, c in XYC:
            cs.append(Circle(x, y, t / c))

        cand = [c.center() for c in cs]
        for i, j in combinations(range(N), r=2):
            p = cs[i].intersection(cs[j])
            if p:
                cand.append(p[0])
                cand.append(p[1])

        ans = 0
        for p in cand:
            tmp = 0
            for c in cs:
                d = c.center().distance(p)
                if d - EPS < c.r:
                    tmp += 1
            ans = max(ans, tmp)
        return ans

    b = Bisect(f)
    return b.bisect_left(K, 0, 10000000)


def main():
    N, K = read_int_n()
    XYC = [read_int_n() for _ in range(N)]
    print(slv(N, K, XYC))


if __name__ == '__main__':
    main()