Calculation of the path traveled by the sparrow

Given the distance between points A and B, the speed of the train moving from A to B, and the speed of the sparrow flying faster than the train, while the train has not yet reached point B, the sparrow makes flights from point B to meet the train and back to point B. Write a program that calculates the total distance traveled by the sparrow in kilometers.

Input data

• distAB – the distance between points A and B (km);
• vTrain – the speed of the train (km/h);
• vSparrow – the speed of the sparrow (km/h), with vSparrow > vTrain.

Output data

• A single number – the total distance traveled by the sparrow, rounded to 2 decimal places.

Example

Input:  100 20 30
Output: 150.00