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 Go (1.6) (judge verdict: Wrong Answer)

package main

import "fmt"

func main() {
	var n, x int64
	fmt.Scanf("%d %d", &n, &x)

	m := countLayers(n)
	fmt.Println(m)

	ds := make([]string, n+1)
	for i := n; i > 0; i-- {
		m = (m - 3) / 2
		if m+2 < x {
			ds[i] = "R"
			x -= m + 2
		} else if m+2 == x {
			ds[i] = "M"
			x -= m + 1
		} else {
			ds[i] = "L"
		}
	}

	fmt.Println(ds)

	ps := make([]int64, n+1)
	ps[0] = 1
	total := int64(0)
	for i := 1; i < len(ds); i++ {
		ps[i] = ps[i-1]*2 + 1
		switch ds[i] {
		case "L":
		case "M", "R":
			total += ps[i-1] + 1
		}
	}

	fmt.Println(total)
}

func countLayers(n int64) int64 {
	if n == 0 {
		return 1
	}
	return 3 + 2*countLayers(n-1)
}