Problem: 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}.

Examples

Input

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


Output

2.4


Input

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


Output

7411.2252

Solution (in PYTHON3):

Solution:
def i1():
 return int(input())
def i2():
 return [int(i) for i in input().split()]
import math
[n,k]=i2()
d=[]
for i in range(n):
 d.append(i2())
eps=10**(-6)
def check(t):
 for x1,y1,c1 in d:
  for x2,y2,c2 in d:
   if x1==x2 and y1==y2:
      continue
   aa=2*(x1-x2)
   bb=2*(y1-y2)
   cc=t**2*(1/c2**2-1/c1**2)+x1**2-x2**2+y1**2-y2**2
   if aa==0:
      continue
   ss=bb**2/aa**2+1
   tt=bb/aa*(x1-cc/aa)-y1
   uu=(x1-cc/aa)**2+y1**2-(t/c1)**2
   if tt**2-ss*uu<0 or ss==0:
      continue
   Y1=-tt-math.sqrt(tt**2-ss*uu)
   Y1/=ss
   X1=(cc-bb*Y1)/aa
   count=0
   for x,y,c in d:
    if c*math.sqrt((X1-x)**2+(Y1-y)**2)<=t+eps:
      count+=1
   if count>=k:
    return True
   Y2=-tt+math.sqrt(tt**2-ss*uu)
   Y2/=ss
   X2=(cc-bb*Y2)/aa
   count=0
   for x,y,c in d:
    if c*math.sqrt((X2-x)**2+(Y2-y)**2)<=t+eps:
      count+=1
   if count>=k:
    return True
 for X,Y,C in d:
   count=0
   for x,y,c in d:
    if c*math.sqrt((X-x)**2+(Y-y)**2)<=t+eps:
      count+=1
   if count>=k:
    return True
 return False

low=0
high=100*3000

while high-low>eps:
  mid=(low+high)/2
  if check(mid):
     high=mid
  else:
     low=mid
print(high)