The cheerful and diligent little fisherman
You're a sailor, I'm a sailor,
You're a fisher, I'm a fisher,
You're on land, I'm at sea,
We won't meet at all!
Seva was in high spirits, humming a cheerful tune as he fished, for the fish were biting like crazy that day...
After another successful catch and releasing the fish back into the water according to all the rules of sport fishing, he pondered an intriguing question: What path does the fish take from the moment it bites to when it's pulled out of the water near the stern?
More precisely: given the length of the fishing rod L (in meters), the casting distance D (in meters), the angle described by the rod during reeling, U (in degrees), the reeling time T (in seconds), and the line reeling speed V (in m/s). During reeling, the line length equals the length of the rod. Throughout the reeling process (the moment of casting the bait is not considered), the rod is in a vertical position. You need to determine the length of the fish's trajectory S (in meters).
Your task is to answer the question that popped into the cheerful and clever Seva's mind.
Input
A single line contains 5 numbers: the length of the fishing rod L (in meters), the casting distance D (in meters), the angle described by the rod during reeling, U (in degrees), the reeling time T (in seconds), and the line reeling speed V (in m/s). During reeling, the line length equals the length of the rod. All input values are non-negative real numbers not exceeding 10^6.
Output
Output a single number - the answer to the problem with a precision of at least 6 decimal places.