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 namespace std;

using ll = long long;

ll f(int N, ll X) {
    ll levelNlen = 1;
    for (int t = 0; t < N; t++) {
        levelNlen = levelNlen *2 + 3;
    }
    ll _levelNlen = (levelNlen - 3) / 2;
    if(N==0) return 1;
    if (X <= 1) return 0;
    ll res = 0;
    if (X <= 1 + _levelNlen) return f(N - 1, X - 1);
    return (1LL<<N)-1 + 1 + (X == 1+_levelNlen+1 ? 0 : f(N-1,X-(1+_levelNlen+1)));
}

int main() {
    int N;
    ll X;
    cin>>N>>X;
    cout << f(N, X) << endl;
}
