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 rep(i,n) for(int i = 0; i < (n);i++)
typedef long long ll;

//パテ　p0 = 1, pi = 2p(i-1)+1 pn = 2^(n+1)-1
//高さ　h0 = 1, hi = 3h(i-1)+2 hn = 2^(n+2)-3

ll rec(int n,ll x){
    if(n==0)return 1;
    ll len = (1LL<<(n+1)) - 3;//n-1レベルのバーガーの高さ
    ll num = (1LL<<n)-1;//n-1レベルのバーガーのパテ数
    if(x == 1)return 0;
    else if(x <= len+1)return rec(n-1,x-1);
    else if(x == len+2)return num+1;
    else if(x <= (len+1)*2)return num+1+rec(n-1,x-len-2);
    else return num*2+1;
}

int main(){
    int N;
    ll X;
    cin >> N >> X;
    ll ans = rec(N,X);
    cout << ans << endl;
    return 0;
}