New Year's Eve Wine Pyramid

At a New Year's Eve party the wine glasses are stacked into a pyramid. The top level holds one glass, the second level holds three, the third holds six, and the fourth holds ten.

Each glass is identified by two numbers, $L$ and $N$. $L$ is the level the glass sits on and $N$ is its number within that level. The glasses on one level form a triangle. They are numbered from the top row downwards, and from left to right within each row.

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

Write a glass on level $L$ as row $r$, position $c$ inside that row, where $1 \le c \le r \le L$. Its number is then $N = r(r-1)/2 + c$.

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

Once a glass is full, the wine that overflows splits equally among the three glasses on the level below that touch it, and none of it spills outside. Wine never flows into a neighbour on the same level, and it never skips a level. When the glass $(r, c)$ on level $L$ overflows, the wine runs into the glasses $(r, c)$, $(r+1, c)$ and $(r+1, c+1)$ on level $L+1$. For example, when the glass with $L = 2$ and $N = 2$ overflows, the wine runs into glasses 2, 4 and 5 on level 3.

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

The first line contains the number of test cases $T$. Each of the next $T$ lines holds one test case with three integers $B$, $L$ and $N$ separated by spaces. $B$ is the number of bottles the bartender pours, $L$ is the level of the glass, and $N$ is the number of the glass on 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.

• $1 \le T \le 150$
• $1 \le B \le 50000$
• $1 \le L \le 400$
• $1 \le N \le L(L+1)/2$