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 C++14 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
#include <iomanip>
#include <vector>
#include <array>
#include <map>
#include <set>
#include <unordered_set>
#include <unordered_map>
#include <string>
#include <algorithm>
#include <limits>
#include <iterator>
#include <cmath>
#include <numeric>
#include <stack>
#include <queue>
#include <cassert>
#include <forward_list>
#include <chrono>
#include <deque>
#include <list>
#include <random>
#include <cstdio>
#include <sstream>

using namespace std;

//最大公約数
template<class T>
inline T GCD(T m, T n)
{
	T temp;
	while (m % n != 0)
	{
		temp = n;
		n = m % n;
		m = temp;
	}
	return n;
}

//最小公倍数
template<class T>
inline T LCM(T m, T n)
{
	return m * n / GCD(m, n);
}



int main()
{
	int n, k; cin >> n >> k;
	
	double ans = 0;
	double p = 1.0 / n;
	for (int i = 1; i < n + 1; i++)
	{
		int count = i;
		int num = 0;
		while (true)
		{
			if (count >= k) { break; }
			count *= 2;
			num++;
		}
		ans += p * pow(1.0/2.0, num);
	}

	cout << fixed << setprecision(12) << ans << endl;
	return 0;
}