# Cricket Clock

Limits 1s, 128 MB

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 $12$, it pauses there for $S$ 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 $N (meter)$ and the freeze time of the second-hand of the clock is $S$, 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 $S$ seconds when pointing at 12.

Note: Spider can move $1 (meter)$ 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.

$PI = 3.14159$

## Input

The first and only line of the input contains two integers $N$ and $S$— represents length of the second-hand of the clock $(meter)$ and amount of time $(seconds)$ it stays still when point at $12$.

$0 \leq N\le 100000$

$1\leq S \leq 100000$

## Output

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 $10^{-8}$. Formally, let your answer be $x$, and the jury's answer be $y$. Your answer is considered correct if $\frac{|x-y|}{max(1,|y|)}\le 10^{-8}$

## Samples

InputOutput
5 5

36.4159000000

InputOutput
7 3

82.3981600000


### Statistics

97% Solution Ratio
esh.29Earliest, 5M ago