Roll an m-sided die n times. Return the expected value of the largest roll.

Easiest through the tail sum. The maximum is at least v unless every roll came in below it:

$$E[\max] = \sum_{v=1}^{m} P(\max \geq v) = \sum_{v=1}^{m}\left(1 - \left(\tfrac{v-1}{m}\right)^{n}\right)$$

Input

n = 2
m = 6

Output

4.472222222222222