Football rivalry (1) P99583

Two long-time rival football teams, let us call them $B$ (for beautiful manners) and $M$ (for miserable manners), are playing again. Both teams are exhausted, so the first to score a goal will win the game for sure. At this moment, team $B$ has the ball. If they decide to go all-in, for a direct attack, there is a probability $w_B$ that they manage to score, thus winning the game. Hovewer, with probability $1 - w_B$ they will lose the ball while their goal is unprotected, and therefore they will lose. Team $B$ has another option: to just pass the ball around. In that case, the possesion of the ball will eventually go to team $M$. Then we will have a simmetrical situation: If team $M$ goes for a direct attack, they will win with probability $w_M$, and they will lose with probability $1 - w_M$. If they decide to just pass the ball and wait, eventually the possesion of the ball will go back to team $B$.

Given $w_B$ and $w_M$, and assuming that both teams take the best decisions (to attack or not to attack) and that team $B$ has the ball now, which is the probability that team $B$ will win?

Input

Input consists of several cases, each with two real numbers $w_B$ and $w_M$, both between 0 and 1. No given probability is $0.5$. The input cases have no precission issues.

Output

For every case, print the probability that team $B$ will win with four digits after the decimal point. If no goal will be scored, state so.