Given is an alphabet $\{0,1,\dots ,k\}$, $0\le k\le 9$. We say that a word of length $n$ over this alphabet is tight if any two neighbour digits in the word do not differ by more than 1.

Input is a sequence of lines, each line contains two integer numbers $k$ and $n$, $1\le n\le 100$. For each line of input, output the percentage of tight words of length $n$ over the alphabet $\{0,1,\dots ,k\}$ with 5 fractional digits.

Sample Input

4 1
2 5
3 5
8 7

Sample Output

100.00000
40.74074
17.38281
0.10130