Problem:
Score : 300 points

Problem Statement

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 1

3 10

Sample Output 1

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.

Sample Input 2

100000 5

Sample Output 2

0.999973749998

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

n ,k = map(int, input().split())

dict ={}

list = []

for i in range(n, 0,-1): # Nから１までのN個の”出目”のリストを作成
    list.append(i)
#print(list)

count_dict = {}
sum = 0
count = 0
i = 0
while(i <= len(list)-1):
    if k // list[i]  <= 2 ** count:
        #print("list is", list[i])
        #print("count is", count)
        #sum += 1 / (2 ** count)
        if count not in count_dict:
            count_dict[count] = 1
        else:
            count_dict[count] += 1
        #print("sum is", sum)
        i += 1
    else:
        count += 1

max_count = max(count_dict)
#print(count_dict)
for i in range(max_count + 1):
    #print(i)
    if i in count_dict:
        sum += count_dict[i] / (2 ** i)
        #print(sum)

print(sum/n)