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