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: Runtime Error)

#![allow(unused_variables)]
#![allow(unused_imports)]
#![allow(dead_code)]
use std::io;
use std::str::FromStr;
use std::iter::FromIterator;
use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::mem::{replace, swap};


// abcde
fn read_string() -> String {
    let mut line = String::new();
    io::stdin().read_line(&mut line).unwrap();
    line
}

// -3.2
fn read_as_primitive<T: FromStr>() -> T {
    let s = read_string();
    s.trim().parse().ok().expect("failed to parse input")
}

// 1 -3 0 999
fn read_as_collection<U: FromStr, T: FromIterator<U>>() -> T {
    let s = read_string();
    s.trim().split_whitespace().map(|s| s.parse().ok().expect("failed to parse")).collect()
}

// #.#.###..
fn read_as_chars<T: FromIterator<char>>() -> T {
    let s = read_string();
    s.trim().chars().collect()
}

// 1 abc
fn read_as_pair<T: FromStr, U: FromStr>() -> (T, U) {
    let s = read_string();
    let elems: Vec<_> = s.trim().split_whitespace().collect();
    (
        elems[0].parse().ok().expect("failed to parse"),
        elems[1].parse().ok().expect("failed to parse"),
    )
}

// 1.5 -2 abc
fn read_as_triple<T: FromStr, U: FromStr, V: FromStr>() -> (T, U, V) {
    let s = read_string();
    let elems: Vec<_> = s.trim().split_whitespace().collect();
    (
        elems[0].parse().ok().expect("failed to parse"),
        elems[1].parse().ok().expect("failed to parse"),
        elems[2].parse().ok().expect("failed to parse"),
    )
}


fn f(n: usize, x: usize, acc: &[usize], acc_patty: &[usize]) -> usize {
    let acc_sub = acc[n - 1];
    let acc_patty_sub = acc_patty[n - 1];
    
    if x <= 1 {
        0
    } else if x <= 1 + acc_sub {
        f(n - 1, x - 1, acc, acc_patty)
    } else if x == 2 + acc_sub {
        1 + acc_patty_sub
    } else if x <= 2 + 2 * acc_sub {
        1 + acc_patty_sub + f(n - 1, x - acc_sub - 2, acc, acc_patty)
    } else {
        // assert_eq!(x, 3 + 2 * acc_sub);
        1 + 2 * acc_patty_sub
    }
}


fn main() {
    let (n, x): (usize, usize) = read_as_pair();
    let mut acc = vec![1; n+1];
    let mut acc_patty = vec![1; n+1];
    for i in 0..n {
        acc[i + 1] = 2 * acc[i] + 3;
        acc_patty[i + 1] = 2 * acc_patty[i] + 1;
    }

    println!("{}", f(n, x, &acc, &acc_patty));
}