Given is an alphabet , . We say that a word of length 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 and , . For each line of input, output the percentage of tight words of length over the alphabet 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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