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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <ctype.h>
#include <string.h>
#include <math.h>

void swap(int * a, int * b)
{
    int t = *a;
    *a = *b;
    *b = t;
}

void print_int(int n)
{
    printf("%d\n",n);
    
}

void sort(int a[], int n)
{
    int h, i, j;

    for(h = 1; h < n / 9; h = h * 3 + 1)
        continue;

    for(; h > 0; h /= 3)
    {
        for(i = h; i < n; i++)
        {
            j = i;
            while(j >= h && a[j] < a[j-h])
            {
                swap(&a[j], &a[j-h]);
                j -= h;
            }
        }
    }
}

void print_list(int a[], int n)
{
    for(int i = 0; i < n; i++)
    {
        printf("%d ", a[i]);
    }
}

void intcpy(int a[], const int b[], int count)
{
    for(int i = 0; i < count; i++)
    {
        a[i] = b[i];
    }
}

int list_sum(int a[], int n)
{
    int sum = 0;

    for(int i = 0; i < n; i++)
    {
        sum += a[i];
    }

    return sum;
}


void permutate(int s[], int count, int n)
{
    if(n == count)
        return;

    for(int i = n; i < count; i++)
    {
        swap(&s[i], &s[n]);

        if(i != n)
        {
            //intcpy(result[j++], s, count);
        }
        
        permutate(s, count, n+1);
        swap(&s[i], &s[n]);
    }
}




int main(void)
{
    int n, k;
    scanf("%d %d", &n, &k);
    double pos = 0;
    for (int i = 1; i <= n; i++)
    {
        double x = ceil(log(k/i)/log(2));
        printf("%lf\n", x);
        pos += (1/(double)n)*pow(0.5,x);
    }
    printf("%lf", pos);

   
   
   

    return 0;
}