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 JavaScript (node.js v5.12) (judge verdict: Accepted)

"use strict";
function main(arg) {
    const inputs = arg.split("\n")
    const N = parseInt(inputs[0].split(" ")[0])
    const X = parseInt(inputs[0].split(" ")[1])
    console.log(func(N,X))
}
function all(level) {
    return Math.pow(2, level + 2) - 3
}
function patty(level) {
    return Math.pow(2, level + 1) - 1
}
function func(level, X) {
    const All = all(level-1)
    if(level === 0){
        return (X === 0) ? 0 : 1
    }else if (X <= 1){
        return 0
    }else if(X <= All + 1){
        return func(level - 1, X - 1)
    }else{
        return patty(level - 1) + 1 + func(level - 1, X - All - 2)
    }
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));