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:
EPS = 10**(-7)
N,K = map(int,input().split())
xyc = [list(map(int,input().split())) for _ in range(N)]

def possible(t):
    res = False
    cand = []
    for i in range(N):
        cand.append(xyc[i][:2])
        x1,y1,c1 = xyc[i]
        r1 = t/c1
        for j in range(i+1,N):
            x2,y2,c2 = xyc[j]
            r2 = t/c2
            d = ((x2-x1)**2+(y2-y1)**2)**0.5
            if abs(r1-r2)+EPS<d<r1+r2-EPS:
                mx = x1+(x2-x1)*(r1**2-r2**2+d**2)/(2*d**2)
                my = y1+(y2-y1)*(r1**2-r2**2+d**2)/(2*d**2)
                l = abs((r1**2-(mx-x1)**2-(my-y1)**2)**0.5)
                nx = (y2-y1)/d
                ny = -(x2-x1)/d
                cand.append([mx+nx*l,my+ny*l])
                cand.append([mx-nx*l,my-ny*l])


    for X,Y in cand:
        n = 0
        for i in range(N):
            x,y,c = xyc[i]
            if c*((X-x)**2+(Y-y)**2)**0.5<t+EPS:
                n += 1
        if n>=K:
            res = True

    return res

ng = 0
ok = 10**6
m = (ng+ok)/2
for i in range(100):
    if possible(m):
        ok = m
    else:
        ng = m
    m = (ok+ng)/2
print(m)