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

int n,x;
int *a,*p;

int burger(int n,int x){
	if(!n)	return (x <= 0 ? 0 : 1);
	else if(x <= 1 + a[n - 1])	return burger(n - 1,x - 1);
	else return p[n - 1] + 1 + burger(n - 1,x - 2 - a[n - 1]);
}

int main(int argc, char const *argv[])
{	
	scanf("%d%d",&n,&x);
	a = (int *)malloc(sizeof(int) * n);
	p = (int *)malloc(sizeof(int) * n);
	a[0] = 1;	p[0] = 1;

	for (int i = 1; i < n; ++i){
		a[i] = a[i - 1] * 2 + 3;
		p[i] = p[i - 1] * 2 + 1;
	}
	printf("%d\n", burger(n,x));
	return 0;
}