P1409 Dice

$n$ people stand in a line, and you are the $m$-th. In each round, the person at the front of the queue rolls a die once. - If they roll $1$, the person at the front wins. - If they roll $2, 4, 6$, the person at the front moves to the end of the queue. - If they roll $3, 5$, the person at the front leaves the queue. If only one person remains in the queue, that person wins. Find the probability that you win.

One line containing two integers $n, m$.

A real number representing the winning probability, to $9$ digits after the decimal point.

- For $30\%$ of the testdata, $0 < m \le n \le 10$. - For $100\%$ of the testdata, $0 < m \le n \le 1000$. Translated by ChatGPT 5