You roll n independent fair dice, each with faces numbered 1 to m. Let X be the largest value shown. Compute the expected value E[X].

Input

Two integers n and m.

Output

Output E[X] with absolute or relative error at most 1e-6.

Constraints

1 <= n <= 10^9

2 <= m <= 10^5

Scoring

This is a standard problem: a submission scores full points if it produces the correct output for every test case, and zero otherwise.

Numeric answers are accepted if they are within an absolute tolerance of 1e-06 or a relative tolerance of 1e-06 of the expected value.