A bag holds fair_coins ordinary coins and double_headed_coins coins with heads on both sides. You draw one coin uniformly at random, flip it n times, and every flip comes up heads. Return the probability that the coin is double-headed.

• a double-headed coin gives n heads with probability 1
• a fair coin gives n heads with probability $(1/2)^n$
• weight each by how many coins of that kind are in the bag

Input

fair_coins = 999
double_headed_coins = 1
n = 10

Output

0.5061789421651013