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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;

public class Main {

    public static void main(String[] args) {

        InputStreamReader isr = new InputStreamReader(System.in);
        BufferedReader br = new BufferedReader(isr);
        PrintWriter out = new PrintWriter(System.out);

        try {
    		String strData = br.readLine();
    		String strDat[] = strData.split(" ", -1);

    		int intMaxDice = Integer.parseInt(strDat[0]);
    		int intWinPoint = Integer.parseInt(strDat[1]);

    		int cmp = 1;
    		int intRole = 0;
    		for (intRole = 0 ; ; intRole++) {
    			if (intWinPoint <= cmp) break;

    			cmp *= 2;
    		}
    		double ans = 0;
    		for (int i = 0 ; i < intMaxDice ; i++) {
    			if (intRole > 0)
    				ans = ans += Math.pow(0.5, intRole);
    			else if (i+1 < intWinPoint)
    				ans = ans += Math.pow(0.5, 1);
    			else
    				ans = ans += 1;

    			intRole --;
    		}

    		ans /= intMaxDice;

    		System.out.print(ans );


    		out.flush();


        } catch (IOException e) {

        }


    }


}