Given is an alphabet \({0, 1, . . . , k}\), \(0 \le k \le 9\). 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

• Input is a sequence of lines, each line contains two integer numbers \(k\) and \(n\), \(1 \le n \le 100\).

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.

Example

Sample input

4 1
2 5
3 5
8 7

Sample output

100.00000
40.74074
17.38281
0.10130