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:

"""
答えをにブタン
円がKこ以上重なる点が生まれる最小のtを求める
どうやって判定する？
"""

def wantnum(m):

    plis = []

    for i in range(N):
        plis.append([xyc[i][0] , xyc[i][1]])

    for i in range(N):
        for j in range(i):

            xA = xyc[i][0]
            yA = xyc[i][1]
            xB = xyc[j][0]
            yB = xyc[j][1]
            r1 = m / xyc[i][2]
            r2 = m / xyc[j][2]

            X = xB-xA
            Y = yB-yA

            a = (X**2 + Y**2 + r1**2 - r2**2) / 2

            retx1 = ( a*X + Y * (( (X**2+Y**2)*(r1**2) - a**2 )**0.5) ) / (X**2 + Y**2)
            rety1 = ( a*Y - X * (( (X**2+Y**2)*(r1**2) - a**2 )**0.5) ) / (X**2 + Y**2)

            retx1 += xA
            rety1 += yA

            retx2 = ( a*X - Y * (( (X**2+Y**2)*(r1**2) - a**2 )**0.5) ) / (X**2 + Y**2)
            rety2 = ( a*Y + X * (( (X**2+Y**2)*(r1**2) - a**2 )**0.5) ) / (X**2 + Y**2)

            retx2 += xA
            rety2 += yA

            if type(retx1) is not complex and type(rety1) is not complex:
                plis.append([retx1,rety1])
            if type(retx2) is not complex and type(rety2) is not complex:
                plis.append([retx2,rety2])

    ans = 0
    for nx,ny in plis:

        nnum = 0

        for i,j,r in xyc:
            if (i-nx)**2 + (j-ny)**2 < (m/r)**2 + 10**(-7):
                nnum += 1

        ans = max(ans,nnum)

    return ans

            

N,K = map(int,input().split())

xyc = []
l = 0
r = 0

for i in range(N):
    
    x,y,c = map(int,input().split())
    xyc.append([x,y,c])

    r = max(r , c * ((x**2+y**2)**0.5) )

while r - l > 10**(-7) and r-l > l * (10**(-7)):

    m = (r+l) / 2

    ret = wantnum(m)
    #print (ret,m)

    if ret >= K:
        r = m
    else:
        l = m

print (r)