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. Sample Input 41 25 35 87 Sample Output 100.00000 40.74074 17.38281 0.10130