Waterloo 2001 Winter B - Tight words

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Points: 7
Time limit: 1.0s
Memory limit: 64M

Problem type

Given is an alphabet \{0, 1, \dots, k\}, 0 \le k \le 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 \le n \le 100. For each line of input, output the percentage of tight words of length n over the alphabet \{0, 1, \dots, 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
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