uva 10900

#include<cstdio>
#include<cstring>
#include<algorithm>
#define maxn 32
using namespace std;
int n;
double p[maxn],t;

void pre()
{
    p[0]=1;
    for(int i=1;i<=30;i++)
        p[i]=p[i-1]*2.0;
}

double solve()
{
    double f=p[n];
    for(int i=n-1;i>=0;i--)
    {
        double eq=p[i]/f;
        if(eq<t)
            f=(1+t)*f/2.0;
        else
            f=(eq-t)*p[i]/(1-t)+(1-eq)*(eq+1)*f/(1-t)/2.0;
    }
    return f;
}

int main()
{
    pre();
    while(scanf("%d%lf",&n,&t)&&n)
    {
        printf("%.3lf\n",solve());
    }
    return 0;
}