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 sys
INF = 1 << 60
MOD = 10**9 + 7 # 998244353
sys.setrecursionlimit(2147483647)
input = lambda:sys.stdin.readline().rstrip()
from cmath import phase, rect
from math import acos
def resolve():
    n, k = map(int, input().split())
    ZC = [None] * n
    for i in range(n):
        x, y, c = map(int, input().split())
        ZC[i] = (complex(x, y), c)

    def check(t):
        # i-th circle : Z[i][0] centered with radius t / Z[i][1]
        circle = [(z, t / c) for z, c in ZC]
        candidate = [c for c, r in circle]
        for c1, r1 in circle:
            for c2, r2 in circle:
                if c1 == c2:
                    continue
                d = abs(c2 - c1)
                alpha = phase(c2 - c1)
                s = (r1**2 + d**2 - r2**2) / (2 * r1 * d)
                if abs(s) >= 1:
                    continue
                theta = acos(s)
                candidate.append(c1 + rect(r1, alpha + theta))
                candidate.append(c1 + rect(r1, alpha - theta))

        return any(sum(abs(z - c) <= r + 0.00001 for c, r in circle) >= k for z in candidate)

    l = 0
    r = 1 << 30
    for _ in range(100):
        m = (l + r) / 2
        if check(m):
            r = m
        else:
            l = m

    print(m)
resolve()