ICC world cup is a prestigious sports event for the cricketer and also for their fans. As a die hard fan of Bangladesh Cricket Team, you don’t miss a match for the world.
Today you went to see a match of your favorite team. As you look at the giant watch tower to see what time it is, you observe some unusual thing. There is a spider on the top of the edge of the second-hand of the clock. It was trying to get to the center of the clock. As the clock is broken like the nearest cricket board, when the second-hand of the clock points at , it pauses there for seconds before beginning its full rotation. This continues for eternity. The spider is scared when the second-hand is rotating so, it doesn’t move. The Spider can only move when the second-hand of the clock stays still. Given the length of the second-hand of the clock and the freeze time of the second-hand of the clock is , can you calculate the total distance the spider covered to reach the center of the clock? You can assume that the second-hand of the clock always moves and only pauses for seconds when pointing at 12.
Note: Spider can move per second. You can assume that, you starts to calculate when the spider was at the edge and the second-hand of the clock was about to go for a full rotation.
The first and only line of the input contains two integers and — represents length of the second-hand of the clock and amount of time it stays still when point at .
Output the total distance covered by the spider from the edge of the second-hand of the clock to the center.
Your answer will be accepted if the absolute or relative error does not exceed . Formally, let your answer be , and the jury's answer be . Your answer is considered correct if
Input | Output |
---|---|
5 5 | 36.4159000000 |
Input | Output |
---|---|
7 3 | 82.3981600000 |