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.

Examples

Input

2 7


Output

4


Input

1 1


Output

0


Input

50 4321098765432109


Output

2160549382716056
#include <bits/stdc++.h>
using i64 = long long;
using std::cout;
using std::endl;
using std::cin;

int main() {
	i64 n, x; scanf("%lld%lld", &n, &x);
	
	i64 p = 1, b = 0;
	for(int i = 0; i < n; i++) {
		p = 2 * p + 1;
		b = 2 * b + 2;
	}
	i64 ans = 0;
	while(p > 1 and x) {
		p = (p - 1) >> 1;
		b = (b - 2) >> 1;
		if(p + b + 1 < x) {
			ans += p + 1;
			x -= p + b + 2;
		} else {
			x--;
		}
	}
	if(x) ans++;
	printf("%lld\n", ans);
	return 0;
}
