#10081Tight 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

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.

4 1
2 5
3 5
8 7

100.00000
40.74074
17.38281
0.10130