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 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

4 1
2 5
3 5
8 7

Output

100.00000
40.74074
17.38281
0.10130