Monsters

An island has three kinds of monsters: red, yellow, and blue. When two monsters of different kinds meet, one eats the other. A red monster eats a yellow monster, a yellow monster eats a blue monster, and a blue monster eats a red monster. Nothing happens when two monsters of the same kind meet.

Exactly two monsters meet at any one moment, and three or more never meet at the same time. At each moment one pair of monsters of different kinds is picked uniformly at random among all such pairs. If $r$ red, $y$ yellow, and $b$ blue monsters are left, the meeting pair is red and yellow with probability $\frac{ry}{ry+yb+br}$, yellow and blue with probability $\frac{yb}{ry+yb+br}$, and blue and red with probability $\frac{br}{ry+yb+br}$.

Repeating this leaves exactly one kind of monster on the island. Compute the probability that each kind is the one that survives.

The first line has the number of test cases $T$. ($1 \le T \le 1000$)

Each of the next $T$ lines has the number of red monsters $r$, the number of yellow monsters $y$, and the number of blue monsters $b$, separated by spaces. ($1 \le r, y, b \le 100$)

For each test case, print one line with the probability that only red monsters survive, the probability that only yellow monsters survive, and the probability that only blue monsters survive, in that order, separated by single spaces.

Round every value to exactly nine digits after the decimal point and keep the trailing zeros. Print 0.333333333 for a probability of $\frac{1}{3}$ and 0.150000000 for 0.15.