Snuke has a fair N-sided die that shows the integers from 1 to N with equal probability and a fair coin. He will play the following game with them:
 - Throw the die. The current score is the result of the die.
 - As long as the score is between 1 and K-1 (inclusive), keep flipping the coin. The score is doubled each time the coin lands heads up, and the score becomes 0 if the coin lands tails up.
 - The game ends when the score becomes 0 or becomes K or above. Snuke wins if the score is K or above, and loses if the score is 0.
You are given N and K. Find the probability that Snuke wins the game.

-----Constraints-----
 - 1 ≤ N ≤ 10^5
 - 1 ≤ K ≤ 10^5
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N K

-----Output-----
Print the probability that Snuke wins the game. The output is considered correct when the absolute or relative error is at most 10^{-9}.

-----Sample Input-----
3 10

-----Sample Output-----
0.145833333333

 - If the die shows 1, Snuke needs to get four consecutive heads from four coin flips to obtain a score of 10 or above. The probability of this happening is \frac{1}{3} \times (\frac{1}{2})^4 = \frac{1}{48}.
 - If the die shows 2, Snuke needs to get three consecutive heads from three coin flips to obtain a score of 10 or above. The probability of this happening is \frac{1}{3} \times (\frac{1}{2})^3 = \frac{1}{24}.
 - If the die shows 3, Snuke needs to get two consecutive heads from two coin flips to obtain a score of 10 or above. The probability of this happening is \frac{1}{3} \times (\frac{1}{2})^2 = \frac{1}{12}.
Thus, the probability that Snuke wins is \frac{1}{48} + \frac{1}{24} + \frac{1}{12} = \frac{7}{48} \simeq 0.1458333333.
[{"code": "import sys\ninput = sys.stdin.readline\nn,k = list(map(int,input().split()))\n#a = list(map(int,input().split()))\n\nimport math\npar = 0\n\nfor i in range(1,n+1):\n    tmp = i\n    cnt = 0\n    while True:\n        if tmp >= k:\n            break\n        tmp *= 2\n        cnt += 1\n    if cnt == 0:par += 1/n\n    else       :par += 1/(2**cnt*n)\n\nprint(f'{par:.12f}')\n", "passed": true, "time": 0.3, "memory": 14276.0, "status": "done"}]