2 1 s 64 MB

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

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 |