Codeforces Round 467 (Div. 2) |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only 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.

brute force

math

number theory

*1400

No tag edit access

The problem statement has recently been changed. View the changes.

×
B. Vile Grasshoppers

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe weather is fine today and hence it's high time to climb the nearby pine and enjoy the landscape.

The pine's trunk includes several branches, located one above another and numbered from 2 to *y*. Some of them (more precise, from 2 to *p*) are occupied by tiny vile grasshoppers which you're at war with. These grasshoppers are known for their awesome jumping skills: the grasshopper at branch *x* can jump to branches .

Keeping this in mind, you wisely decided to choose such a branch that none of the grasshoppers could interrupt you. At the same time you wanna settle as high as possible since the view from up there is simply breathtaking.

In other words, your goal is to find the highest branch that cannot be reached by any of the grasshoppers or report that it's impossible.

Input

The only line contains two integers *p* and *y* (2 ≤ *p* ≤ *y* ≤ 10^{9}).

Output

Output the number of the highest suitable branch. If there are none, print -1 instead.

Examples

Input

3 6

Output

5

Input

3 4

Output

-1

Note

In the first sample case grasshopper from branch 2 reaches branches 2, 4 and 6 while branch 3 is initially settled by another grasshopper. Therefore the answer is 5.

It immediately follows that there are no valid branches in second sample case.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/03/2024 06:38:02 (i1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|