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

//ABC115D
int main(void) {
  long long n, x, k, i, cou=0, pcu=0, tmp;
  scanf("%lld %lld", &n, &x);
  long long thi[n+1], p[n+1];
  thi[0]=1, p[0]=1;
  for(i=1; i<=n; i++){
    thi[i]=thi[i-1]*2+3, p[i]=p[i-1]*2+1;
  }
  i=n;
  while(cou<x&&i>=0){
    if(x>=cou+thi[i]){

      cou+=thi[i];
      pcu+=p[i];
      if(x>=cou+1) cou++, pcu++;
      //printf("thi[%lld]=%lld p[%lld]=%lld", i, thi[i], i, p[i]);
      //printf(" cou=%lld pcu=%lld\n", cou, pcu);
    }else{
      cou++;
      //printf("thi[%lld]=%lld p[%lld]=%lld", i, thi[i], i, p[i]);
      //printf(" cou=%lld pcu=%lld\n", cou, pcu);
      i--;
    }
  }
  printf("%lld", pcu);
}