#2531 Tight words

1 s   64 MB  

Description

Given is an alphabet {0, 1, ... , k}, 0 <= k <= 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

Input is a sequence of lines, each line contains two integer numbers k and n, 1 <= n <= 100.

Output

For each line of input, output the percentage of tight words of length n over the alphabet {0, 1, ... , k} with 5 fractional digits.

Sample Input

Sample Output

4 1
2 5
3 5
8 7
100.00000
40.74074
17.38281
0.10130

Source

Waterloo local 2001.01.27