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 (1.15.1) (judge verdict: Accepted)

use std::str::FromStr;
use std::fmt::Debug;

fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

fn solve(n: usize, x: u64, layer: &Vec<u64>, patty: &Vec<u64>) -> u64{
    if x == 0{
        return 0;
    }else if x == 1{
        if n == 0{
            return 1;
        }else{
            return 0;
        }
    }else if x <= layer[n-1]+1{
        return solve(n-1, x-1, layer, patty);
    }else if x == layer[n-1] + 2{
        return 1 + patty[n-1];
    }else if x <= 2*layer[n-1] + 2{
        return 1 + patty[n-1] + solve(n-1, x - 2 - layer[n-1], layer, patty);
    }else{
        return patty[n];
    }
}

fn main(){
    let line: Vec<u64> = read_as_vec();
    let (n, k) = (line[0], line[1]);
    let mut layer: Vec<u64> = vec![0;(n+1) as usize];
    let mut patty: Vec<u64> = vec![0;(n+1) as usize];
    layer[0] = 1;
    patty[0] = 1;
    for i in 1..(n+1) as usize{
        layer[i] = layer[i-1]*2+3;
    }
    for i in 1..(n+1) as usize{
        patty[i] = patty[i-1]*2+1;
    }

    let ans = solve(n as usize, k, &layer, &patty);
    println!("{}", ans);
}