Problem:
Score : 400 points

Problem Statement

In some other world, today is Christmas.

Mr. Takaha decides to make a multi-dimensional burger in his party. A level-L burger (L is an integer greater than or equal to 0) is the following thing:

A level-0 burger is a patty.

A level-L burger (L \geq 1) is a bun, a level-(L-1) burger, a patty, another level-(L-1) burger and another bun, stacked vertically in this order from the bottom.

For example, a level-1 burger and a level-2 burger look like BPPPB and BBPPPBPBPPPBB (rotated 90 degrees), where B and P stands for a bun and a patty.

The burger Mr. Takaha will make is a level-N burger. Lunlun the Dachshund will eat X layers from the bottom of this burger (a layer is a patty or a bun). How many patties will she eat?

Constraints

1 \leq N \leq 50

1 \leq X \leq ( the total number of layers in a level-N burger )

N and X are integers.

Input

Input is given from Standard Input in the following format:

N X

Output

Print the number of patties in the bottom-most X layers from the bottom of a level-N burger.

Sample Input 1

2 7

Sample Output 1

4

There are 4 patties in the bottom-most 7 layers of a level-2 burger (BBPPPBPBPPPBB).

Sample Input 2

1 1

Sample Output 2

0

The bottom-most layer of a level-1 burger is a bun.

Sample Input 3

50 4321098765432109

Sample Output 3

2160549382716056

A level-50 burger is rather thick, to the extent that the number of its layers does not fit into a 32-bit integer.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
class P{
    static long[] leng=new long[51];
    // l+ = 2l+3
    //l0=1
    //l=
    static long count(long sou,long nagasa){
        if(sou==0)return(nagasa==1?1:0);
        if(nagasa<=1)return 0;
        if(nagasa<=leng[sou-1]+1)return(count(sou-1,nagasa-1));
        if(nagasa==leng[sou-1]+2)return(count(sou-1,leng[sou-1])+1);
        if(nagasa==leng[sou])return(2*count(sou-1,leng[sou-1])+1);
        return(count(sou-1,leng[sou-1])+1+count(sou-1,nagasa-2-leng[sou-1]));
    }
    static void Main(){
        leng[0]=1;
        for(int i=1;i<=50;i++){
            leng[i]=3+2*leng[i-1];
        }
        var s=Console.ReadLine().Split().Select(long.Parse).ToArray();
        Console.WriteLine(count(s[0],s[1])); 
    }
}