Vampire Dice

Vampire is a popular roleplaying game. Like most roleplaying games, Vampire uses dice to settle random events. The most common use of the dice is deciding whether you succeeded or failed at a task. A task might be shooting another player, staying inside a window instead of falling out of it, or dodging an opponent's hit.

The dice used in Vampire are 10-sided, and the rules are these. You may roll $x$ dice, and you need $y$ or more points to succeed. A die showing 8, 9 or 10 earns one point, so 1 through 7 earn nothing. On top of that, a 10 earns one extra roll. That is why two points or more are possible even when you start with a single die.

Here is an example. Truls tries to avoid falling into a trap. To succeed she has to score 4 or more points on 5 dice. Her first roll gives two 10s, a 4, a 6 and a 3. That is only two points, but the two 10s give her two more dice. This time she rolls a 10 and a 2. She now has three points and one more die. The last die lands on 5, and Truls falls into a big pit and dies.

How large was Truls' chance of surviving in the first place? Write a program that computes the probability of success from the number of dice and the point requirement.

The first line contains the number of cases $n$ ($1 \le n \le 100$).

Each of the next $n$ lines contains two integers $x$ and $y$, where $x$ is the number of dice you start with ($0 \le x \le 100$) and $y$ is the number of points needed to succeed ($0 \le y \le 100$).

For each case, print the probability of success on its own line, rounded to three decimal places and printed with exactly three digits after the decimal point.

No case has a probability that lands exactly on a rounding boundary, so there is no question of which way to break a tie.