Background

Special for beginners, ^_^

Description

Many balls fall one by one down a full binary tree ($FBT$, $Full\ Binary\ Tree$). At each moment, a falling ball first visits a non-leaf node. As it continues to fall, it goes either into the right subtree or the left subtree, until it reaches a leaf node. The direction a ball takes is determined by the boolean value stored at each node. Initially all nodes are $false$. When a ball visits a node: if the node is $false$, the ball sets it to $true$ and then continues its journey down the left subtree; if the node is $true$, the ball sets it to $false$ and then continues down the right subtree. The labeling of the full binary tree is shown in the figure below.

Because all nodes are initially $false$, the first ball visits node $1$, node $2$ and node $4$, toggles their boolean values, and finally stops at node $8$. The second ball visits node $1$, node $3$ and node $6$, and stops at node $12$. Clearly, before it stops, the third ball visits node $1$, node $2$ and node $5$, and stops at node $10$.

Your task: given the depth $D\$ of the $FBT$ and $I$ (meaning the $I$-th ball is dropped; you may assume $I$ does not exceed the number of leaves of the given $FBT$), write a program that finds the leaf number at which the ball stops.

Format

Input

The input consists of a single line containing two integers $D$ and $I$ separated by a space, where $2\le D \le 20，1\le I\le 524288$.

Output

Output the leaf number at which the $I$-th ball stops.

Samples

4 2

12

Limitation

1s, 1024KiB for each test case.