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 <vector>
#include <cmath>
#include <queue>
#include <deque>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <ctime>
#include <functional>
#include <bitset>
#include <utility>
#include <sstream>
#include <fstream>
#include <stack>
#include <cstdlib>
#include <complex>
#include <set>
#include <iomanip>

using namespace std;

#define INF 1070000000LL
#define pb push_back
#define irep(i,a,b) for(int i=a;i<b;i++)
#define rep(i,n) irep(i,0,n)

typedef long long lint;
typedef pair<int, int> pint;
typedef vector<vector<pint> > Graph;


int main(){
    int n,k;
    cin >> n >> k;
    double result = 0.0;
    rep(i,n){
	if(k <= i+1){
	    result += 1;
	    continue;
	}
	else{
	    double tmp = (double)k/(i+1);
	    int rp = ceil(log2(tmp));
	    result += pow(0.5,rp);
	}
    }
    result /= (double)n;
    cout << setprecision(9) << result << endl;
}