CSES - Candy Lottery
  • Time limit: 1.00 s
  • Memory limit: 512 MB
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.

Constraints
  • $1 \le n \le 100$
  • $1 \le k \le 100$
Example

Input:
2 3

Output:
2.444444