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 = 1e-7
N, K = map(int, input().split())
pts = []
Cs = []
for _ in range(N):
    x, y, c = map(int, input().split())
    pts.append(x + y * 1j)
    Cs.append(c)

Rs = [0] * N


def cands():
    for i in range(N):
        yield pts[i]
        for j in range(i + 1, N):
            pt = pts[j] - pts[i]
            ab = -2 * pt
            l = ab * ab.conjugate()
            c = pt * pt.conjugate() + Rs[i] - Rs[j]
            d = Rs[i] - c * c / l
            if d.real < 0:
                continue
            m = (d / l) ** 0.5
            off = m * (ab.imag - ab.real * 1j)
            yield -ab * c / l + off + pts[i]
            yield -ab * c / l - off + pts[i]


def ok(secs):
    for i in range(N):
        Rs[i] = secs * secs / Cs[i] / Cs[i]
    for cand in cands():
        count = 0
        for pt, r in zip(pts, Rs):
            xy = pt - cand
            if (xy * xy.conjugate()).real < r + EPS:
                count += 1
                if count == K:
                    return True
    return False


lo = 0
hi = 1e10
for _ in range(100):
    mid = (lo + hi) / 2
    if ok(mid):
        hi = mid
    else:
        lo = mid
print(hi)