New Year's Eve Wine Pyramid

Wine glasses are stacked in a pyramid at a new year's party. The top level holds one glass, the level below it holds three, the next holds six, and the one after that holds ten. The picture below shows the shape.

A glass is identified by two numbers, $L$ and $N$. $L$ is the level the glass sits on and $N$ is the number of the glass inside that level. Glasses on a level are numbered like this:

Level 1:
    1

Level 2:
    1
 2     3

Level 3:
      1
   2     3
4     5     6

Level 4:
         1
      2     3
   4     5     6
7     8     9     10

Level $L$ is a triangle of rows holding 1 glass up to $L$ glasses, so it has $\frac{L(L+1)}{2}$ glasses. The glass in position $j$ of row $i$ has number $\frac{i(i-1)}{2} + j$.

Each glass holds 250ml of wine. The bartender pours wine into the top glass ($L = 1$, $N = 1$) from bottles of 750ml each.

Once a glass is full, the wine that no longer fits overflows in equal parts into the three glasses of the next level that touch it, and nothing is spilled outside. Wine never overflows sideways into a glass on the same level, and it never falls straight past the next level. Wine that overflows from the glass in position $j$ of row $i$ on level $L$ reaches position $j$ of row $i$, position $j$ of row $i+1$, and position $j+1$ of row $i+1$ on level $L+1$. For example, when the glass with $L = 2$ and $N = 2$ overflows, the wine reaches the glasses with $L = 3$ and $N$ equal to 2, 4 and 5.

After the bartender has poured all $B$ bottles, find how much wine in ml the glass with number $N$ on level $L$ holds.

The first line has the number of test cases, $T$. $T$ test cases follow. Each test case is three integers $B$, $L$ and $N$. $B$ is the number of bottles the bartender pours, $L$ is the level the glass sits on and $N$ is the number of the glass inside that level.

For each test case print one line in the form "Case #x: y", where $x$ is the test case number starting from 1 and $y$ is the amount of wine in ml in that glass. Round $y$ to seven decimal places and print all seven digits, including trailing zeros.

• $1 \le T \le 150$
• $1 \le B \le 1000$
• $1 \le L \le 100$
• $1 \le N \le \frac{L(L+1)}{2}$