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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::{input, fastout};

struct Helper {
  memo: Vec<(usize, usize)>
}

impl Helper {
  fn traverse(&self,
    index: usize,
    mut val: usize,
    mut total: usize
  ) -> usize {
    if val == 1 {
      return total
    }
    val -= 1;
    
    let (b_p, b_b) = self.memo[index-1];
    let last = b_p + b_b;
    if val < last {
      return self.traverse(index-1, val, total);
    } else if val == last {
      return total + b_b;
    }
    val -= last;
    total += b_b;
    
    if val == 1 {
      return total + 1;
    }
    val -=1;
    total +=1;
    
    if val < last {
      return self.traverse(index-1, val, total);
    } else if val == last {
      return total + b_b;
    }
    val -= last;
    total += b_b;
    
    if val == 1 {
      return total
    }
    
    panic!("total: {}, val: {}, index: {}", total, val, index);
  }
}

#[fastout]
fn main() {
  input! {
    n: usize,
    x: usize,
  }
  
  let mut memo: Vec<(usize, usize)> = vec![];
  memo.push((0, 1));
  
  for i in 1..=n {
    let a = memo[i-1].0 * 2usize + 2usize;
    let b = memo[i-1].1 * 2usize + 1usize;
    memo.push((a, b));
  }
  let helper = Helper { memo };
  let result = helper.traverse(n, x, 0);  

  println!("{}", result);
}