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