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 C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<stdint.h>
#include<inttypes.h>

typedef int32_t i32;
typedef int64_t i64;

void run (void) {
  i64 n, x;
  scanf ("%" SCNi64 "%" SCNi64, &n, &x);
  i64 *len = (i64 *) calloc (n, sizeof (i64));
  i64 *p = (i64 *) calloc (n, sizeof (i64));
  len[0] = p[0] = 1;
  for (i32 i = 1; i < n; ++i) {
    len[i] = 2 * len[i - 1] + 3;
    p[i] = 2 * p[i - 1] + 1;
  }
  i64 ans = 0;
  for (i32 i = n; x > 0; --i) {
    x--;
    if (x < len[i - 1]) continue;
    x -= len[i - 1];
    ans += p[i - 1];
    if (x == 0) break;
    x--;
    ans++;
    if (x < len[i - 1]) continue;
    x -= len[i - 1];
    ans += p[i - 1];
    break;
  }
  printf ("%" PRIi64 "\n", ans);
}

int main (void) {
  run();
  return 0;
}