Prize

Prize

Segtree entered a programming contest with a team of $N$ and won a $K$ yen prize! I'm trying to distribute this prize now.

Each $N$ team member, including Segtree, is numbered from $1$ to $N$ in order of ability. Segtree is $1$.

If the prize amount of $i$'s teammate $(i \ geq 2)$ is less than "$i-half of the prize amount of$ i's teammate rounded down to an integer", that person Get angry.

When distributing the $K$ Yen prize so that no one gets angry, find the maximum prize that Segtree can get.

input

Input is given from standard input in the following format.

N K

output

Please output the maximum prize money that Segtree can receive.

However, insert a line break at the end.

Constraint

• $1 \ leq N, K \ leq 10 ^ {18}$
• All inputs are integers.

Input example 1

1 1

Output example 1

1

Input example 2

819875141880895728 349993004923078537

Output example 2

174996502461539284

Example

Input

1 1

Output

1

inputFormat

input

Input is given from standard input in the following format.

N K

outputFormat

output

Please output the maximum prize money that Segtree can receive.

However, insert a line break at the end.

Constraint

• $1 \ leq N, K \ leq 10 ^ {18}$
• All inputs are integers.

Input example 1

1 1

Output example 1

1

Input example 2

819875141880895728 349993004923078537

Output example 2

174996502461539284

Example

Input

1 1

Output

1

样例

1 1

1