A clearing of firewood#5182
A young boy named Fermá lives in a village. With cold evenings approaching, his grandmother has asked him to gather firewood from the forest. Near Fermá's village, there is a magical Clearing of Firewood where the supply is endless. Naturally, Fermá needs to go there.
The challenge is that the Clearing is not very close, and traveling through the forest is much slower than moving across the field where the village is located.
The village is situated at the coordinates (, ).
The Clearing is located at the coordinates (, ).
The boundary between the forest and the field is a horizontal line y = a, where is a number (0 \leq a \leq 1).
The speed across the field is V_p, and the speed through the forest is V_f. Along the boundary, movement can occur either through the forest or across the field.
Determine the point at which Fermá should enter the forest to reach the Clearing of Firewood in the shortest possible time.
The first line of the input contains two positive integers - V_p and V_f (1 \leq V_p, V_f \leq 10^5). The second line contains a single real number - the axis coordinate of the boundary between the forest and the field (0 \leq a \leq 1).
Output a single real number with a precision of at least decimal places - the axis coordinate of the point where Fermá should enter the forest.
Example 1