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