Heracles and the Stables of Augeas

Heracles faced twelve labors. The fifth was not as dramatic as slaying a giant serpent: he had to clean the stables of Augeas, home to more than 1000 cattle and untouched for 30 years, in a single day.

Instead of shoveling by hand, he diverted nearby rivers through the stables. You are given several rivers, each described as a polyline with a water supply. Choose which rivers to divert so the stables receive at least $W$ units of water while minimizing total digging distance.

For each chosen river, Heracles digs one straight canal from the stable to the closest point on that river. Canals may cross each other or other rivers, and he cannot merge canals to save work.

The first line contains an integer $K$, the number of data sets. Each data set follows.

The first line of a data set has integers $n$ and $W$, then floating-point coordinates $x$ and $y$ of the stables. $1 \leq n \leq 100$, $0 \leq W \leq 100$, and $(x, y)$ is the stable location.

Each of the next $n$ lines describes one river. It starts with integer $k_i$ ($2 \leq k_i \leq 20$), the number of points, then integer $w_i$ ($1 \leq w_i \leq 100$), the water supplied. The remaining $2k_i$ numbers are the coordinates $(x_j, y_j)$ of the river points in order.

For data set $x$, print Data Set x: on its own line, then on the next line print the minimum total digging distance to obtain at least $W$ water, rounded to two decimals. If the rivers cannot supply enough water together, print Impossible. Leave a blank line after each data set.