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)

fn main() {
    let s = std::io::stdin();
    let mut sc = Scanner { reader: s.lock() };
    let n: usize = sc.read();
    let mut num = vec![0; n + 1];
    let mut p = vec![0; n + 1];
    num[0] = 1;
    p[0] = 1;
    for i in 0..n {
        num[i + 1] = 3 + 2 * num[i];
        p[i + 1] = 1 + 2 * p[i];
    }

    let x: usize = sc.read();

    println!("{}", eat(n, x, &num, &p));
}

fn eat(level: usize, mut x: usize, num: &Vec<usize>, p: &Vec<usize>) -> usize {
    if x == 0 {
        0
    } else if level == 0 {
        match x {
            0 => 0,
            1 => 1,
            _ => unreachable!(),
        }
    } else {
        assert!(x > 0);
        if x >= num[level] - 1 {
            return p[level];
        }
        let mut ans = 0;
        let next = num[level - 1];
        x -= 1;
        if x < next {
            return eat(level - 1, x, num, p);
        }
        x -= next;
        ans += p[level - 1];
        if x == 0 {
            return ans;
        }
        x -= 1;
        ans += 1;
        if x < next {
            return eat(level - 1, x, num, p) + ans;
        }
        unreachable!()
    }
}

pub struct Scanner<R> {
    reader: R,
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .reader
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n')
            .take_while(|&b| b != b' ' && b != b'\n')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn read_vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}