Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Karen and Neighborhood

time limit per test

2 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputIt's been long after the events of the previous problems, and Karen has now moved on from student life and is looking to relocate to a new neighborhood.

The neighborhood consists of *n* houses in a straight line, labelled 1 to *n* from left to right, all an equal distance apart.

Everyone in this neighborhood loves peace and quiet. Because of this, whenever a new person moves into the neighborhood, he or she always chooses the house whose minimum distance to any occupied house is maximized. If there are multiple houses with the maximum possible minimum distance, he or she chooses the leftmost one.

Note that the first person to arrive always moves into house 1.

Karen is the *k*-th person to enter this neighborhood. If everyone, including herself, follows this rule, which house will she move into?

Input

The first and only line of input contains two integers, *n* and *k* (1 ≤ *k* ≤ *n* ≤ 10^{18}), describing the number of houses in the neighborhood, and that Karen was the *k*-th person to move in, respectively.

Output

Output a single integer on a line by itself, the label of the house Karen will move into.

Examples

Input

6 4

Output

2

Input

39 3

Output

20

Note

In the first test case, there are 6 houses in the neighborhood, and Karen is the fourth person to move in:

- The first person moves into house 1.
- The second person moves into house 6.
- The third person moves into house 3.
- The fourth person moves into house 2.

In the second test case, there are 39 houses in the neighborhood, and Karen is the third person to move in:

- The first person moves into house 1.
- The second person moves into house 39.
- The third person moves into house 20.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/22/2018 11:06:15 (d3).

Desktop version, switch to mobile version.

User lists

Name |
---|