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Problem 1342 Tight Words

Accept: 108    Submit: 202
Time Limit: 1000 mSec    Memory Limit : 32768 KB

Problem 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

4 1 2 5 3 5 8 7

Sample Output

100.00000 40.74074 17.38281 0.10130

Source

Waterloo 010127

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