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 (1.42.0) (judge verdict: Accepted)

use proconio::input;

#[proconio::fastout]
fn main() {
    input! {
        N: i128,
        X: i128
    }
    println!("{}", search(N, X));
}

fn search(level: i128, remaining: i128) -> i128 {
    if remaining <= 0 { return 0 }
    return if remaining >= length(level) {
        patty(level)
    } else if remaining > length(level - 1) + 1 {
        patty(level - 1) + 1 + search(level - 1, remaining - 2 - length(level - 1))
    } else {
        search(level - 1, remaining - 1)
    };
}

fn patty(n: i128) -> i128 { return (2i128 << n) - 1; }

fn length(n: i128) -> i128 { return (4i128 << n) - 3; }