Candy Lottery

There are n children, and each of them independently gets a random integer number of candies between 1 and k. What is the expected maximum number of candies a child gets?

Input

The only input line contains two integers n and k.

Output

Print the expected number rounded to six decimal places (rounding half to even).

Constraints

$1 \le n \le 100$

$1 \le k \le 100$

Example

Input

2 3

Output

2.444444