Preparation

For this assignment you will need functions from the math module. You can find more information about this in your text book on page 67 and 68. Also, try the interactive session underneath in the Python shell. The first command imports the math module, so it can be used. The second command shows the help information about the math module. You can go through this document with the space bar. You can close the document by pressing Q. Once you find the correct function, you can ask for more information about it as is demonstrated in the function pow.

>>> import math
>>> help(math)
>>> help(math.pow)

Assignment

When sending parcels, the tariff is calculated as follows:
The weight in kilograms of the parcel is first rounded up, so that it becomes a whole number. For a parcel of two kilograms or less, you pay a standard fee of $$s$$ euros. For every extra kilogram (on top of the maximum of two kilograms), an extra fee of $$t$$ euros per kilogram is charged.

Input

The value of $$s$$ and $$t$$ (in euros) and the weight of a parcel (in kilograms). In this order on separate lines.

Output

The total cost to send the parcel given.

Example

Input:

1.99
1.42
666.01

Output:

946.29