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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
#define FOR(i,a,b) for (int i=(a);i<(b);i++)
#define rep(i,n) FOR(i,0,n)
typedef long long ll;

ll L[52] = {};
ll P[52] = {};
void make() {
	// layers
	L[0] = 1;
	FOR(i, 1, 51) {
		L[i] = 2*L[i-1] + 3; 
	}

	// p
	P[0] = 1;
	FOR(i, 1, 51) {
		P[i] = 2*P[i-1] + 1;
	}
}

ll layers_p_x(ll i, ll x) {
	if (i==0) {
		if (x==1) {
			return 1;
		} else {
			return 0;
		} 
	}
	if (x <= L[i-1] + 1) {
		return layers_p_x(i-1, x-1);
	}
	if (L[i] == x) {
		return P[i];
	}
	//return layers_p(i) - layers_p_x(i-1, layers(i) - x - 1);
	return 1 + P[i-1] + layers_p_x(i-1, x-2-L[i-1]);
}
int main(){
	ll n,x;
	cin >> n>>x;
	make();
	cout << layers_p_x(n,x) << endl;
	return 0;
}