**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 (rounding half to even).

# Constraints

- 1 \le n \le 100
- 1 \le k \le 100

# Example

Input:

2 3

Output:

2.444444