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>
long long result = 0;
long long int two[55] = {}, hum[55] = {}, ban[55] = {};
int a=0;
long long int hantei(long long int num, long long int eat) {
  if(a==1){return 0;}
	if (eat >= 3 && num == 0&&a==0) { result += 3; return 0; }
  
	if (eat == hum[num] + 1) {
		result += ban[num];
		result++;
		return 0;
	}

	if (eat >= hum[num]) {
		eat -= hum[num];
		result += ban[num];

		if (eat == 0) { return 0; }
		result++;
		eat--;

	}

	if (eat == 0) { return 0; }
  if (num == 0) {  a=1;}
	hantei(num - 1, eat - 1);
}
int main() {
	long long int n, x;

	two[0] = 1;
	hum[0] = 1;
	ban[0] = 1;
	for (int i = 1; i <= 50; i++) {
		two[i] = 2 * two[i - 1];
		hum[i] = 2 * hum[i - 1] + 3;
		ban[i] = 2 * ban[i - 1] + 1;
	}
	scanf("%lld%lld", &n, &x);
	
	
	hantei(n, x);
		printf("%lld",result);
}