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CSES Problem Set

Candy Lottery


Task | Statistics


CSES - Candy LotteryCSES - 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
Example

Input:
2 3

Output:
2.444444