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:
N,K = map(int,input().split())
XYC = [list(map(int,input().split())) for _ in [0]*N]
eps = 1e-7
def f(x,y,t):
    ret = 0
    for X,Y,C in XYC:
        if ((x-X)**2+(y-Y)**2)<=(t/C)**2+eps: ret += 1
    return ret

def get_cross_section(x1,y1,r1,x2,y2,r2):
    d = ((x1-x2)**2+(y1-y2)**2)**0.5
    X = (d*d+r1*r1-r2*r2)/(2*d)
    Y = max(0,(r1*r1-X*X))**0.5
    dx = (x2-x1)/d
    dy = (y2-y1)/d
    ret = [(x1+X*dx+Y*dy,y1+X*dy-Y*dx)]
    if Y>0 : ret.append((x1+X*dx-Y*dy,y1+X*dy+Y*dx))
    return ret
def check(t):
    kouho = []
    for i in range(N):
        x1,y1,c1 = XYC[i]
        kouho.append((x1,y1))
        for j in range(i+1,N):
            x2,y2,c2 = XYC[j]
            tmp = get_cross_section(x1,y1,t/c1,x2,y2,t/c2)
            for tmp2 in tmp:
                kouho.append(tmp2)
    for tmp in kouho:
        if f(tmp[0],tmp[1],t) >= K:return True
    return False

l=0
r=1000000
for _ in range(100):
    i = (l+r)/2
    if check(i):
        r = i
    else:
        l = i
print(r)