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: Accepted)

function Main(input) {
  input = input.split("\n");
  var N = parseInt(input[0].split(" ")[0]);
  var X = parseInt(input[0].split(" ")[1]);
  bans=new Array(50);
  all=new Array(50);
  bans[0]=1;
  all[0]=1;
  var ans = 0;
  for(i=1;i<=50;i++){
    bans[i]=bans[i-1]*2+1;
    all[i]=all[i-1]*2+3;
  }
  var full=all[N];
  var bs=bans[N];
  var flag=0;
  if(X%2==0){
    X=all[N]-X;
    flag=1;
  }
  while(X>0&&full>0){

    if(X>(full-1)/2){
      X=X-(full-1)/2-1;
      ans=ans+(bs-1)/2+1;
      full=(full-1)/2-1;
      bs=(bs-1)/2
    }else{
      X=X-1;
      full=(full-1)/2-1;
      bs=(bs-1)/2
    }
  }
  if(flag==1){
    ans=bans[N]-ans;
  }
  console.log('%s', ans);
}
  
// "実行する"ボタンを押した時に実行される関数 (デバッグ用)
function debug(){
  var input = document.getElementById("input").value;
  Main(input);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));