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: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

typedef char                SINT8;
typedef unsigned char       UINT8;
typedef short               SINT16;
typedef unsigned short      UINT16;
typedef int                 SINT32;
typedef unsigned int        UINT32;
typedef long long           SINT64;
typedef unsigned long long  UINT64;

#define MAX(a,b) ((a)>(b)?(a):(b))
#define MIN(a,b) ((a)<(b)?(a):(b))
#define ABS(a) ((a)>(0)?(a):-(a))


SINT32 main() {
    SINT64 ans = 0;
    SINT32 max = 10;

    SINT32 L;
    SINT64 eat;

    

    scanf("%d%lld",&L,&eat);

    SINT64 data[51];
    SINT64 all[51];
    SINT32 buf = 0;

    data[0] = 1;
    for (SINT32 i = 1; i < 51; i++) {
        data[i] = data[i-1]*2+1;
    }

    all[0] = 1;
    for (SINT32 i = 1; i < 51; i++) {
        all[i] = all[i-1]*2+3;
    }

    SINT32 LAST = 0;
    for (SINT32 i = L-1; i >= -1; i--) {

        if ( eat == all[i+1] + 1 ) {
            ans = ans + data[i+1];
 //           printf("A\n");
            break;
        } else if (eat == all[i+1] + 2) {
            ans = ans + data[i+1] + 1; 
 //           printf("B\n");
            break;
        } else if (eat > all[i+1] + 1) {
            ans = ans + data[i+1] + 1;
            eat = eat - all[i+1] - 2;
            LAST = 1;
            if (i == -1) {
                ans = ans + 1;
            }

 //           printf("%lldJJ\n",eat);
        } else {
            if (LAST == 1 ) {
                eat = eat-1;
            }
            
        }



 //       printf("%lld\n",ans);
    }


    printf("%lld\n",ans);
	return 0;
}