Hook or Be Hooked

Judding loves fishing but has grown bored with the ordinary kind, so he proposed a new style called veteran fishing to the members of his club: fishing takes place at a small lake or pond instead of a wide riverbank or seashore. Each angler stays fixed at one spot on land and catches fish living in the nearby water with a long rod. A rod that casts farther is better, so a better rod always helps.

Let the farthest reachable casting distance be the fishing distance, denoted $R$. A fishing ground is called a valid ground when its whole polygon lies inside the circle centered at Judding's seat $Z = (0, 0)$ with radius $R$. Computing $d = x^2 + y^2$ for every vertex shows that a ground is valid exactly when the largest of those values is at most $R^2$.

Figure 1. A layout with $N = 6$ and $K = 5$.

Judding has a limited budget, so he wants to upgrade his rod only up to the point where at least $K$ valid grounds are secured from his seat. In the figure above, a fishing distance of $11$ or more secures five valid grounds, so the economical choice is the smallest such value, $11$.

Given the polygonal outlines of all fishing grounds, compute the smallest fishing distance that secures at least $K$ valid grounds.

The first line contains the number of fishing grounds $N$ and the required minimum number of valid grounds $K$, separated by a space. $1 \le N, K \le 100000$ and $K \le N$. Then the descriptions of the $N$ grounds follow in order. Each ground is described in two lines.

• The first line contains the number of vertices $P_i$ of the polygon.
• The second line contains the vertex coordinates as integers in the order $x$ $y$, separated by spaces. The vertices are given in clockwise or counterclockwise order starting from the first point.
• Distinct grounds never overlap, and every polygon has positive area and does not intersect itself.

Let $R$ be the smallest fishing distance that secures at least $K$ valid grounds. Print the value of $R^2$, rounded to two digits after the decimal point (rounding half up at the third digit).

The third sample uses the same layout as the figure in the statement.