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:
def main():
    import sys
    sys.setrecursionlimit(10**9)
    input = sys.stdin.readline
    from math import hypot
    from collections import deque

    N, K = map(int, input().split())
    XYC = [tuple(map(int, input().split())) for _ in range(N)]

    dq = deque([(0, 0, 1000.0)])

    ans = 10**18
    while dq:
        X, Y, r = dq.popleft()
        c_hypot = [c * hypot(max(abs(X - x) - r, 0), max(abs(Y - y) - r, 0)) for x, y, c in XYC]
        c_hypot.sort()
        if ans * 0.9999995 > c_hypot[K-1]:
            c_hypot = [c * hypot(X - x, Y - y) for x, y, c in XYC]
            c_hypot.sort()
            if c_hypot[K-1] < ans:
                ans = c_hypot[K-1]

            r /= 2
            dq += [
                (X + r, Y + r, r),
                (X - r, Y + r, r),
                (X + r, Y - r, r),
                (X - r, Y - r, r),
            ]
    print(ans)

main()