Score : $600$ points
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.
Input is given from Standard Input in the following format:
$N$ $K$ $x_1$ $y_1$ $c_1$ $\vdots$ $x_N$ $y_N$ $c_N$
Print the answer.
It will be considered correct if its absolute or relative error from our answer is at most $10^{-6}$.
4 3 -1 0 3 0 0 3 1 0 2 1 1 40
2.4
If we put the heat source at $\left(-0.2, 0\right)$, the $1$-st, $2$-nd, and $3$-rd pieces of meat will be ready to eat within $2.4$ seconds. This is the optimal place to put the heat source.
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
7411.2252