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)

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn main() {
    let v = read_vec::<u64>();
    let (n, x) = (v[0], v[1]);
    let n = n as usize;
    let mut p_count = vec![0u64; n + 1];
    p_count[0] = 1;
    for i in 1..n + 1 {
        p_count[i] = p_count[i - 1] * 2 + 1;
    }

    let mut size_count = vec![0u64; n + 1];
    size_count[0] = 1;
    for i in 1..n + 1 {
        size_count[i] = size_count[i - 1] * 2 + 3;
    }

    let mut ans = 0u64;
    let mut x = x;
    for i in (1..n + 1).rev() {
        if x <= 1 {
            break;
        }
        x -= 1;
        if x == size_count[i - 1] {
            ans += p_count[i - 1];
            break;
        }
        if x == size_count[i - 1] + 1 {
            ans += p_count[i - 1] + 1;
            break;
        }
        if x >= 2 * size_count[i - 1] {
            ans += p_count[i];
            break;
        }
        if x > size_count[i - 1] {
            ans += p_count[i - 1] + 1;
            x -= size_count[i - 1] + 1;
        }
    }
    println!("{}", ans);
}