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:
from math import hypot

def solve():
    N, K = map(int, input().split())
    xs, ys, cs = [], [], []
    for _ in range(N):
        x, y, c = map(int, input().split())
        xs.append(x)
        ys.append(y)
        cs.append(c)

    EPS = 10**-10
    def isLE(a, b):
        return not (a > b+EPS)

    def getIntersectionLCs(a, b, c, xC, yC, r):
        e = a*xC + b*yC + c
        ab2 = a**2 + b**2
        v = r**2 * ab2 - e**2
        if v < 0:
            return []
        elif v == 0:
            xP = xC + -a*e / ab2
            yP = yC + -b*e / ab2
            return [(xP, yP)]
        else:
            v = v**0.5
            ae, be = a*e, b*e
            av, bv = a*v, b*v
            xP1 = xC + (-ae + bv) / ab2
            yP1 = yC + (-be - av) / ab2
            xP2 = xC + (-ae - bv) / ab2
            yP2 = yC + (-be + av) / ab2
            return [(xP1, yP1), (xP2, yP2)]

    def getIntersectionCCs(x1, y1, r1, x2, y2, r2):
        xC, yC = x2-x1, y2-y1
        c = -(xC**2 + yC**2 + r1**2 - r2**2) / 2
        intCCs = getIntersectionLCs(xC, yC, c, 0, 0, r1)
        intCCs = [(x1 + x, y1 + y) for x, y in intCCs]
        return intCCs

    def countNum(xP, yP, xs, ys, rs, K):
        num = 0
        for i, (x, y, r) in enumerate(zip(xs, ys, rs), start=1):
            dist = hypot(x-xP, y-yP)
            if isLE(dist, r):
                num += 1
            if num >= K:
                return True
            elif num+N-i < K:
                return False
        return num >= K

    def isOK(t):
        rs = [t/c for c in cs]

        for xP, yP in zip(xs, ys):
            if countNum(xP, yP, xs, ys, rs, K):
                return True

        for i in range(N):
            x1, y1, r1 = xs[i], ys[i], rs[i]
            for j in range(i+1, N):
                x2, y2, r2 = xs[j], ys[j], rs[j]
                intCCs = getIntersectionCCs(x1, y1, r1, x2, y2, r2)
                for xP, yP in intCCs:
                    if countNum(xP, yP, xs, ys, rs, K):
                        return True

        return False

    ng, ok = 0, 2*10**5
    while abs(ok-ng) > 10**-7:
        mid = (ng+ok) / 2
        if isOK(mid):
            ok = mid
        else:
            ng = mid

    print(ok)


solve()