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: Runtime Error)

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

typedef struct burger{
	int type;//0:bread, 1:pudding
	struct burger *next;
	struct burger *back;
}BG;

BG* master;//一番上

void after_insert_list(BG* p){
	BG* newp;
	newp = (BG*)malloc(sizeof(BG));
	newp->type=-1;
	newp->next=p->next;
	newp->back=p;
	p->next=newp;
}

BG* makeburger(long int level, BG* p){
	if(level==0){
		after_insert_list(p);
		p->next->type=1;
		return p->next;
	}
	else{
		after_insert_list(p);
		p->next->type=0;
		p=makeburger(level-1, p->next);
		after_insert_list(p);
		p->next->type=1;
		p=makeburger(level-1, p->next);
		after_insert_list(p);
		p->next->type=0;
	}
}

int main(){
	int N, X;
	scanf("%d %d", &N, &X);
	master = (BG*)malloc(sizeof(BG));
	master->next=NULL;
	master->back=NULL;
	master->type=-1;
	BG* newp;
	newp = makeburger(N, master);
	//printf("%p %d %p %p\n", newp, newp->type, newp->next, newp->back);
	long int i=0, count=0;
	while(i<X){
		if(newp->type==-1) continue;
		else if(newp->type==1){
			count++;
		}
		newp=newp->back;
		i++;
	}
	printf("%ld", count);
}