题目描述

Problem B: Tight words

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.

样例 1

输入

4 1
2 5
3 5
8 7

输出

100.00000
40.74074
17.38281
0.10130

题目来源：fps-zhblue-waterloo-010127.xml；FPS 共享题包，题包内第 2 题。保留原作者与原赛事署名。