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: Wrong Answer)

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <utility>
#include <numeric>
#include <array>
#include <cmath>
#include <memory>
using namespace std;
//変数デバッグ
#define DEB(variable) cout << #variable << '=' << variable << endl

//for簡易表記(引数ミス防止)
#define FOR(LoopVariable,numberOFbegin,numberOFend) for (int LoopVariable = (numberOFbegin); (LoopVariable) < (numberOFend); (LoopVariable)++)
#define DEFOR(LoopVariable,numberOFbegin,numberOFend) for (int LoopVariable = (numberOFbegin)-1; (LoopVariable) >= (numberOFend); (LoopVariable)--)
#define REP(LoopVariable,numberOFend) for(int LoopVariable = 0;(LoopVariable)<(numberOFend);LoopVariable++)

constexpr long long int linf = numeric_limits<long long int>::max()-5;
constexpr int inf= numeric_limits<int>::max()-5;
constexpr long long int mod = 1000000007;

int main(){

    int n, k;
    cin >> n >> k;
    double result = 0,this_prob;
    int now_score;
    FOR(i,1,n+1){
        this_prob = 1.0;
        now_score = i;

        while(now_score<k){
            now_score *= 2;
            this_prob /= 2.0;
        }
        result += this_prob;
    }
    cout << result/n << endl;

    return 0;
}