Level Hamburger

Time limit0.5sMemory limit512 MB

Summary

A level-N burger is defined recursively from buns and patties; count how many patties lie in the bottom X layers.

Level: Medium5 of 10
Topics: Recursion, Divide and conquer, Math, Implementation
Solved: No attempts yet

Problem

Sanggeun Nald has released a new hamburger, the level-L burger. A level-L burger is made as follows.

A level-0 burger consists of a single patty.
A level-L burger consists of a bun, a level-(L-1) burger, a patty, a level-(L-1) burger, and a bun, in that order. (L ≥ 1)

For example, a level-1 burger looks like 'BPPPB' and a level-2 burger looks like 'BBPPPBPBPPPBB'. (B is a bun, P is a patty.)

Sangdo visits Sanggeun Nald and orders a level-N burger. If Sangdo eats the bottom X layers of the hamburger, how many patties does he eat? One layer is one bun or one patty.

Input

The first line gives N and X.

Output

Print the number of patties Sangdo eats on the first line.

Constraints

1 ≤ N ≤ 50
1 ≤ X ≤ the number of layers in a level-N burger

Examples3

Example 1
Input
```
2 7
```
Expected output
```
4
```
Example 2
Input
```
1 1
```
Expected output
```
0
```
Example 3
Input
```
50 4321098765432109
```
Expected output
```
2160549382716056
```