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;

long long rec(int N, long long X) {
  if (N == 0) {
    if (X == 0) return 0;
    if (X == 1) return 1;
  }
  // レベル N-1 のバンとパティ
  long long bp = (1LL << (N+1)) - 3;
  // レベル N-1 のパティ
  long long p = (1LL << N) - 1;
  if (X == 1) return 0;
  else if (X <= 1 + bp) return rec(N-1, X-1);
  else if (X == 1 + bp + 1) return p + 1;
  else if (X <= 2 + 2*bp) return p + 1 + rec(N-1, X-2-bp);
  else return 2*p + 1;
}

int main() {
  int N; cin >> N;
  long long X; cin >> X;
  cout << rec(N, X) << endl;
}