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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

fun burger_count(lv:Int):Pair<Long,Long>{
    if(lv == 0){
      return Pair(1L, 1L);
    }
    val (patty,all) = burger_count(lv - 1);
    return Pair(patty * 2 + 1L, all * 2 + 3L);
}
fun eat_patty(lv:Int,remain_eat:Long):Pair<Long,Long>{
  if (remain_eat == 0L){
    return Pair(0,0);
  }
  if(lv == 0){
    println("" + lv +"all");
    return Pair(1,remain_eat-1);
  }
  else{
    if (remain_eat < 1){
      return Pair(0,0);
    }else{
      val (p,a) = burger_count(lv - 1);
      if(a * 2 < remain_eat - 3){
        return Pair(p * 2 + 1,remain_eat - 3 - (a * 2));
      }else if(a <= remain_eat - 2){
         val (peatedd,rd) = eat_patty(lv - 1,remain_eat - 2 - a);
         return Pair(p + peatedd + 1,rd);
      }else{
         return eat_patty(lv - 1,remain_eat - 1);
      }
    }
  }  
}


fun main(args: Array<String>) {
    val (n,x) = readLine()!!.split(" ").map { num ->num.toLong() };   
    
    val (eat,all) = eat_patty(n.toInt(),x);
    
    println(eat);
}