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 (GCC 5.4.1) (judge verdict: Accepted)

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

typedef long long int int64;

int64 length[51];
int64 cnt[51];

int64 calc(int64 level,int64 *x){
  if(*x==0) return 0;
  if(*x>=length[level]){
    *x-=length[level];
    return cnt[level];
  }
  int64 res=0;
  (*x)--;
  res+=calc(level-1,x);
  if(*x<=0) return res;
  (*x)--;
  res++;
  res+=calc(level-1,x);
  if(*x<=0) return res;
  (*x)--;
  return res;
}

void run(void){
  int n;
  int64 x;
  scanf("%d%lld",&n,&x);
  length[0]=cnt[0]=1;
  int i;
  for(i=1;i<=n;i++){
    length[i]=2*length[i-1]+3;
    cnt[i]=2*cnt[i-1]+1;
  }
  int64 ans=calc(n,&x);
  printf("%lld\n",ans);
}

int main(void){
  run();
  return 0;
}