题目描述

When I was young, my father is a senior gaming enthusiast. One day, we saw a old man in the street. He had a dice and played with other people.

Every turn the gambler gives $k$ RMB to the old man and throw the dice. If the point is $1$, $2$ or $3$, he will win $2k$ RMB back, otherwise he will get nothing.

My father told me, “I can win all his money by the following strategy”.

“Each turn, I bet on $1$ RMB first. If I lose, I will bet on $2$ RMB. If I still lose, I will bet on $4, 8, 16, \dots$, and so on, until I win. And start to bet on $1$ RMB, do the same thing again.”

“If I don't have enough money to bet, I will bet on all my money.”

Now the question is, if the dice is even, my father has $n$ RMB, the old man has $m$ RMB, they stop until one of them lose all his money, what’s the probability of my father’s victory.

输入格式

The input contains multiple test cases. (No more than $20$)

In each test case:

The only line contains two numbers $n$, $m$. ($0 \le n,m \le 2000000$), indicate my father’s money and the old man’s. We guarantee $\max(n,m) \ge 1$.

输出格式

For each test case, print the answer in five decimal.

1 0
3 3

1.00000
0.50000