Suit Distribution

Bridge is a four-player card game (two teams of two) with many intricate conventions that even experienced players struggle to keep track of. Fortunately, none of those conventions matter here; you do not even need to know how to play the game.

What does matter is that the way a single suit is distributed between your two opponents often decides whether your line of play succeeds. For example, suppose you and your partner together hold 8 cards of the spade suit. Because each suit has 13 cards, the remaining 5 spades are held by your two opponents and can be split as 0-5, 1-4, or 2-3. Note that a 0-5 split can happen in two ways: opponent 1 holds no spade and opponent 2 holds all 5, or the other way around.

Strong players often choose their line of play based on the most likely distribution, so knowing the probability of each split is useful whenever you have to guess.

Assume the 52 cards of the deck are dealt uniformly at random so that each of the four players gets 13 cards, and that you know exactly which 26 cards your team holds (so your two opponents hold the other 26 cards).

The input consists of several queries. Each query is a line with two integers $a$ and $b$ ($0 \le a, b \le 13$ and $a + b \le 13$). The input ends with a line containing $a = b = -1$, which must not be processed.

For each query, print one line in the format <a>-<b> split: <p>, where the leading a and b are the two input numbers written in the given order, and p is a probability printed with exactly 8 digits after the decimal point.

$p$ is the probability that the $a + b$ cards of the suit held by your opponents split so that one opponent holds $a$ of them and the other holds $b$; assume the remaining $13 - (a + b)$ cards of that suit are held by you and your partner. When $a \ne b$, the two orderings ($a$-$b$ and $b$-$a$) are distinct deals and both count toward this probability.