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 read_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim_right().to_owned()
}

fn str_to_ints(s: String) -> std::vec::Vec<i64> {
    let mut ret = std::vec::Vec::new();
    let ws = s.split_whitespace();
    for w in ws {
        ret.push(w.parse().unwrap());
    }
    ret
}

fn read_ints() -> std::vec::Vec<i64> {
    str_to_ints(read_line())
}

fn bp_num(n: i64) -> i64 {
    if n == 0 {
        return 1;
    } else {
        return 2 * bp_num(n - 1) + 3;
    }
}

fn p_num(n: i64) -> i64 {
    if n == 0 {
        return 1;
    } else {
        return 2 * p_num(n - 1) + 1;
    }
}

fn dfs(n: i64, x : i64) -> i64 {
    if n == 0 {
        return 1;
    }

    let bp_num_nm1 = bp_num(n - 1);
    let p_num_nm1 = p_num(n - 1);

    if x == 0 {
        return 0;
    } else if x == bp_num(n) - 1 {
        return p_num(n);
    } else if x == 1 + bp_num_nm1 {
        return p_num_nm1 + 1;
    } else if x > 1 + bp_num_nm1 {
        return p_num_nm1 + 1 + dfs(n - 1, x - bp_num_nm1 - 2);
    } else {
        return dfs(n - 1, x - 1);
    }
}
fn main() {
    let nx = read_ints();
    let n = nx[0];
    let x = nx[1];

    println!("{}", dfs(n, x - 1));
}