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::io::*;
use std::str::FromStr;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let n: usize = read();
    let x: usize = read();
    // BPPPB
    //
    let mut size = 5;
    let mut pcnt = 3;
    let mut map: Vec<(usize, usize)> = vec![(0, 0)];
    for i in 0..n {
        map.push((size, pcnt));
        size = size * 2 + 3;
        pcnt = pcnt * 2 + 1;
    }
    let ans = dfs(n, x, &map);
    println!("{}", ans);
}

fn dfs(n: usize, x: usize, map: &Vec<(usize, usize)>) -> usize {
    if n == 1 {
        return match x {
            5 | 4 => 3,
            3 => 2,
            2 => 1,
            _ => 0,
        };
    }
    if x >= map[n].0 - 1 {
        return map[n].1;
    }

    if x > map[n - 1].0 + 2 {
        return map[n - 1].1 + 1 + dfs(n - 1, x - map[n - 1].0 - 2, &map);
    }

    if x == map[n - 1].0 + 2 {
        return map[n - 1].1 + 1;
    }

    if x > 1 {
        return dfs(n - 1, x - 1, &map);
    }
    return 0;
}