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 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
inline int read(){
	int sum=0,fushu=1;
	char c=getchar();
	while(!isdigit(c)){
		if(c=='-') fushu=-fushu;
		c=getchar();
	}
	while(isdigit(c)){
		sum=sum*10+(c^48);
		c=getchar();
	}
	return sum*fushu;
}
void write(int x){//只能输出非负整数！！！比赛的时候看清楚！！！ 
	if(x>=10) write(x/10);
	putchar(x%10+48);
}
inline void writeln(int x){
	write(x);
	putchar('\n');
}
int n,k;
long double ans;
int main(){
	scanf("%d%d",&n,&k);
	for(int i=1;i<=n;i++){
		int temp=i;
		long double tot=1.0;
		while(temp<=k-1)
		  temp<<=1,tot/=2.0;
		ans+=tot;
	}
	printf("%.12Lf\n",ans/n);
	return 0;
}