Cutting Cheese

A cheese processing company built a machine that cuts a spherical cheese into slices of exactly equal weight. The next target is Swiss cheese, which has holes in it.

A cheese such as Emmentaler contains holes of different sizes. A slice with many holes holds less cheese, so it weighs less. The problem is how to cut a cheese with holes into slices of equal weight.

Sonar scanning locates the holes down to micrometer precision. In this problem every hole is a perfect sphere. The cheese has uniform density, so the weight of a slice is proportional to the volume of cheese in it.

An uncut block is a cube $100$ millimeters on each side. Cut it into $s$ slices of equal weight. Every slice is $100$ millimeters wide and $100$ millimeters high, and you have to determine the thickness of each slice.

The first line contains the number of holes $n$ and the number of slices $s$, where $0 \le n \le 10\,000$ and $1 \le s \le 100$.

Each of the next $n$ lines contains four positive integers $r$, $x$, $y$, and $z$ describing one hole. Here $r$ is the radius and $(x, y, z)$ is the center, all measured in micrometers.

The block occupies the points with $0 \le x, y, z \le 100\,000$ that belong to no hole. The cuts are perpendicular to the $z$ axis.

Holes do not overlap, but they may touch each other. Every hole lies entirely inside the cheese and may touch its boundary.

Print the thickness of each of the $s$ slices in millimeters, one per line, starting from the $z = 0$ end of the block.

Round each thickness to nine places after the decimal point and print exactly nine digits after the decimal point.