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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		String line = reader.readLine();
		String[] str = line.split(" ");
		int n = Integer.parseInt(str[0]);
		int k = Integer.parseInt(str[1]);
		double ans = 0.0;
		for (int i = 1; i <= n; i++) {
			int zyo = 0;
			int zz = i;
			outer:
			for (int z = 1; z <= k;  z++) {
				if (zz >= k) {
					break outer;
				}
				zz *= 2;
				zyo ++;
			}
//			if (i == k) {
//				zyo = 0;
//			}
//			else if (i > 1) {
//			    zyo = (int) Math.floor(Math.log(k) / Math.log(i));
//			}
//			else {
//				zyo = (int) Math.floor(Math.log(k) / Math.log(2)) + 1;
//			}
//			System.out.println("i=" + i + ", zyo=" + zyo);   ////////////////////
			ans += Math.pow(0.5, zyo);
		}
		ans /= n;
		System.out.println(ans);
	}
}