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 math
def intersectionCC0(x1, y1, r1, r2):
    r = x1**2 + y1**2
    t = (r + r1**2 - r2**2) / (2*r)
    dd = r1**2/r - t**2
    if - (10**-8) < dd < 0: dd = 0
    if dd < 0: return []
    x, y = t * x1, t * y1
    if dd == 0: return [(x, y)]
    sq = math.sqrt(dd)
    dx, dy = y1 * sq, -x1 * sq
    return [(x+dx, y+dy), (x-dx, y-dy)]

def intersectionCC(x1, y1, x2, y2, r1, r2):
    return [(x1+x, y1+y) for x, y in intersectionCC0(x2-x1, y2-y1, r1, r2)]

def chk(t):
    L = [a for a in L0]
    for i, (x1, y1, c1) in enumerate(X):
        for x2, y2, c2 in X[:i]:
            L += intersectionCC(x1, y1, x2, y2, t/c1, t/c2)
    for x0, y0 in L:
        cnt = 0
        for x, y, c in X:
            if math.sqrt((x-x0) ** 2 + (y-y0) ** 2) * c <= t + 10**-8:
                cnt += 1
        if cnt >= K: return 1
    return 0

N, K = map(int, input().split())
X = []
L0 = []
for _ in range(N):
    x, y, c = map(int, input().split())
    X.append((x, y, c))
    L0.append((x, y))

l, r = 0, 150000
while (r-l) * (1<<20) > max(1, l):
    m = (l+r) / 2
    if chk(m):
        r = m
    else:
        l = m
    
print((l+r)/2)