Magic Knights

You have $k$ chess knights, and you want to place them on a certain number of chessboards of size $n\times n$ in such a way that no pair of knights is attacking each other.

Because you are a very economical person, you are interested in the minimum number of chessboards of size $n\times n$ that need to be purchased in order to accommodate at least $k$ chess knights in total.

A chess knight is a piece that can move in the following way in one move:

Input

The first line contains two integers $n$, $k$ ($1\le n\le 10^9$, $1\le k\le 10^{18}$).

Output

Output a single number in one line — the answer to the problem.

Examples

Note

An example of one of the optimal knight placements in the first test:

Scoring

In this problem, there are conditional blocks. If your solution works correctly for certain constraints, it will receive a certain number of points. Note that the evaluation is still in testing.

1. ($8$ points): $n\le 5,k\le 20$;

2. ($30$ points): $n,k\le 10^6$;

3. ($28$ points): $n,k\le 10^9$;

4. ($34$ points): without additional constraints.