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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int main(void){
  int N,i;
  long long int num[52],patty[50],X,site,eat,center;
  char str[100],*p;
  
  fgets(str,sizeof(str),stdin);
  p=strtok(str," \n");
  N=atoi(p);
  p=strtok(NULL," \n");
  X=atol(p);
  
  for(i=1,num[0]=1,patty[0]=1;i<N+1;i++){
    num[i]=2*num[i-1]+3;
    patty[i]=2*patty[i-1]+1;
  }
  site=num[N],i=N,eat=0;
  
  while(i>=0){
    center=num[i]/2+1;
    if(X==num[i]){
      eat+=patty[i];
      break;
    }
    if(X==0){
      break;
    }
    if(X<center){
      X-=1;
      i--;
    }else if(X>center){
      eat+=patty[i-1]+1;
      X-=center;
      i--;
    }else{
      eat+=patty[i-1]+1;
      break;
    }
  }
  
  printf("%lld\n",eat);
  
  
  return 0;
}