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 JavaScript (node.js v5.12) (judge verdict: Runtime Error)

function main(input){
    lines = input.split(" ");

    var N = lines[0];
    var X = lines[1];
    var l="131";

    if(N==0){
        l="1";
    }else if(N==1){
        l="131";
    }else{
        for(var i=0;i<N-1;i++){
            var r = l.charAt(0);
            l = l.slice(1);
            l = l.slice(0,-1);
            var t =1 + Number(r);
            var b = "" + t + l + r + 1 + r + l +t;
            l=b;
        }
    }

    var enco=0;
    var ans=0;
    var sub=0;
    for(var i=0;i<X;i++){
        enco+=Number(l.charAt(i));
        if(enco>X){
            break;
        }
        i++;
        sub=Number(l.charAt(i));
        enco += sub;
        ans += sub;
        if(enco>=X){
            var u = enco - X;
            ans-=u;
            break;
        }
    }

    console.log(ans);

}

main(require('fs').readFileSync('/dev/stdin','utf8'));