#描述#
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.

#格式#
##输入格式##

##输出格式##

#样例1#
##样例输入1##

4 1
2 5
3 5
8 7

##样例输出1##

100.00000
40.74074
17.38281
0.10130

#限制#
1000ms
1024KB

#提示#

#来源#