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
    from math import sqrt, hypot
    input = sys.stdin.readline

    def dist(p1, p2):
        return hypot(p1[0]-p2[0], p1[1]-p2[1])

    def CP(x1, y1, r1, x2, y2, r2):
        rr0 = (x2 - x1) ** 2 + (y2 - y1) ** 2
        xd = x2 - x1
        yd = y2 - y1
        rr1 = r1 ** 2
        rr2 = r2 ** 2
        cv = (rr0 + rr1 - rr2)
        if 4 * rr0 * rr1 - cv ** 2 >= 0:
            sv = sqrt(4 * rr0 * rr1 - cv ** 2)
            return (
                (x1 + (cv * xd - sv * yd) / (2. * rr0), y1 + (cv * yd + sv * xd) / (2. * rr0)),
                (x1 + (cv * xd + sv * yd) / (2. * rr0), y1 + (cv * yd - sv * xd) / (2. * rr0)),
            )
        else:
            return (x1, y1), (x2, y2)

    N, K = map(int, input().split())

    if N == 1:
        print(0)
        exit()

    info = []
    for _ in range(N):
        info.append(tuple(map(int, input().split())))

    eps = 10**-8
    ok = 150000.
    ng = -eps
    mid = (ok+ng)/2
    while ok - ng > 10**-7:
        cp_list = []
        flg = 0
        fin = 0
        for i in range(N):
            x1, y1, c1 = info[i]
            p1 = (x1, y1)
            r1 = mid / c1
            for j in range(i+1, N):
                x2, y2, c2 = info[j]
                p2 = (x2, y2)
                r2 = mid / c2
                pa, pb = CP(x1, y1, r1, x2, y2, r2)
                cp_list.append(pa)
                cp_list.append(pb)

        flg = 0
        for p0 in cp_list:
            tmp = 0
            for x, y, c in info:
                p = (x, y)
                r = mid / c
                if dist(p0, p) < r + eps:
                    tmp += 1
            if tmp >= K:
                flg = 1
                break

        if flg:
            ok = mid
        else:
            ng = mid
        mid = (ok+ng)/2
    print(ok)


if __name__ == '__main__':
    main()