How Much Does Bagging Reduce Variance?

Before Ardwick Mutual pays to run a panel of models instead of one, someone asks what the panel actually buys. A single model's estimate for the same claim moves from one training run to the next: retrain it on a different resample of the history and the number comes out different. That wobble is the model's prediction variance, and it is precisely the part of the error a panel is supposed to remove, since several models wobbling independently can cancel each other out. The desk wants the theoretical figure before it commits to the compute bill.

Task: Print the prediction variance the panel is expected to have.

Input

One line holding two values separated by a single space: the single model's prediction variance, then m, the number of models on the panel, as a whole number.

Output

One line holding the panel's expected variance rounded to 4 decimal places. Assume the m models' wobbles are entirely unrelated to one another. On that assumption the variance shrinks by the full factor of m — the panel size itself, not its square root and not one less than it.

Example:

Input:
4.0 4

Output:
1.0000