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:
import sys
input = sys.stdin.readline
from math import sqrt

N,K=map(int,input().split())
M=[tuple(map(int,input().split())) for i in range(N)]

def cross_coor(x0,y0,c0,x1,y1,c1): # 二円の交点
    if (c1-c0)**2<=(x1-x0)**2+(y1-y0)**2<=(c0+c1)**2:
        x2,y2=x1-x0,y1-y0
        a=(x2**2+y2**2+c0**2-c1**2)/2

        xa=(a*x2+y2*sqrt((x2**2+y2**2)*(c0**2)-a**2))/(x2**2+y2**2)+x0
        ya=(a*y2-x2*sqrt((x2**2+y2**2)*(c0**2)-a**2))/(x2**2+y2**2)+y0

        xb=(a*x2-y2*sqrt((x2**2+y2**2)*(c0**2)-a**2))/(x2**2+y2**2)+x0
        yb=(a*y2+x2*sqrt((x2**2+y2**2)*(c0**2)-a**2))/(x2**2+y2**2)+y0

        return [(xa,ya),(xb,yb)]
    else:
        return False

OK=1<<31
NG=0

while OK-NG>10**(-8):
    mid=(OK+NG)/2
    
    CANDI=[]
    for i in range(N):
        x0,y0,c0=M[i]
        CANDI.append((x0,y0))
        for j in range(i+1,N):
            x1,y1,c1=M[j]
            CR=cross_coor(x0,y0,mid/c0,x1,y1,mid/c1)
            if CR:
                CANDI.extend(CR)

    for z,w in CANDI:
        count=0
        for x,y,c in M:
            if (c**2)*((x-z)**2+(y-w)**2)<=(mid+10**(-8))**2:
                count+=1
            
        if count>=K:
            OK=mid
            break
    else:
        NG=mid

print((OK+NG)/2)