Tight Words

Consider the alphabet ${0, 1, \ldots, k}$ where $0 \le k \le 9$. A word of length $n$ over this alphabet is called tight if every pair of neighbouring digits differs by at most $1$.

The input consists of several lines. Each line contains two integers $k$ and $n$ ($0 \le k \le 9$, $1 \le n \le 100$). Process each line in order until the end of input (EOF).

For each input line, print the percentage of tight words of length $n$ over the alphabet ${0, 1, \ldots, k}$. That is, the number of tight words divided by the total number of words $(k+1)^n$, multiplied by $100$. Print the value rounded to exactly $5$ fractional digits (ties, i.e. $0.5$, round up).