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;
use utils::*;

pub fn main() {
    let i = stdin();
    let mut o = Vec::new();
    run(i.lock(), &mut o);
    stdout().write_all(&o).unwrap();
}

fn run<R: BufRead, W: Write>(i: R, o: &mut W) {
    let mut i = CpReader::new(i);
    let (n, x) = i.read2::<usize, usize>();

    writeln!(o, "{}", solve(n, x)).unwrap();
}
fn solve(n: usize, x: usize) -> usize {
    fn eat(lvs: &[(usize, usize)], n: usize, x: &mut usize, r: &mut usize) {
        if *x == 0 {
            return;
        }
        if *x >= lvs[n].0 {
            *x -= lvs[n].0;
            *r += lvs[n].1;
            return;
        }
        if n == 0 {
            *x -= 1;
            *r += 1;
            return;
        }

        *x -= 1;
        if *x == 0 {
            return;
        }
        eat(lvs, n - 1, x, r);
        if *x == 0 {
            return;
        }
        *x -= 1;
        *r += 1;
        if *x == 0 {
            return;
        }
        eat(lvs, n - 1, x, r);
        if *x == 0 {
            return;
        }
        *x -= 1;
    }
    let mut lvs = Vec::new(); // (層数, パティ枚数)
    lvs.push((1, 1));
    for _ in 0..n + 1 {
        let l = lvs.iter().cloned().last().unwrap();
        lvs.push((l.0 * 2 + 3, l.1 * 2 + 1));
    }
    let mut r = 0;
    let mut x = x;
    eat(&lvs, n, &mut x, &mut r);
    r
}

mod utils {
    use super::*;

    pub struct CpReader<R: BufRead> {
        r: R,
        s: String,
    }

    macro_rules! fn_read {
        { $f:ident($($t:ident),*) } => {
            #[allow(dead_code)]
            pub fn $f<$($t: FromStr),*>(&mut self) -> ($($t),*) {
                let i = &mut self.read_line().split(' ');
                ($(read_next::<$t,_>(i)),*)
            }
        };
    }

    impl<R: BufRead> CpReader<R> {
        pub fn new(r: R) -> Self {
            CpReader {
                r: r,
                s: String::new(),
            }
        }
        pub fn read_line(&mut self) -> &str {
            self.s.clear();
            self.r.read_line(&mut self.s).unwrap();
            self.s.trim()
        }

        fn_read! { read2(T1, T2) }
        fn_read! { read3(T1, T2, T3) }
        fn_read! { read4(T1, T2, T3, T4) }
        fn_read! { read5(T1, T2, T3, T4, T5) }
    }
    fn read_next<'a, T: FromStr, I: Iterator<Item = &'a str>>(i: &mut I) -> T {
        i.next().unwrap().parse().ok().unwrap()
    }
}