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: Wrong Answer)

#include <stdio.h>
typedef long long ll;

int main(void){
    ll n,x,ans=0;
    scanf("%lld%lld",&n,&x);
    ll count=1,countp=1;
    for (int i=0; i<n; i++){
        count=count*2+3;
        countp=countp*2+1;
    }
    for (int i=n; i>0; i--){
        if (x>count){
            ans+=countp;
            x-=count;
            if (x>0){
                    ans++;
                    x--;
                } else {
                    break;
                }
                if (x>0){
                    x-=1;
                } else {
                    break;
                }
        } else {
            if (x>0){
                x--;
            } else {
                break;
            }
        }
        count=(count-3)/2;
        countp=(countp-1)/2;
    }
    
    printf("%lld\n",ans+x);
	return 0 ;
}