Please subscribe to the official Codeforces channel in Telegram via the link: https://t.me/codeforces_official.
×

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

A. Cloning Toys

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputImp likes his plush toy a lot.

Recently, he found a machine that can clone plush toys. Imp knows that if he applies the machine to an original toy, he additionally gets one more original toy and one copy, and if he applies the machine to a copied toy, he gets two additional copies.

Initially, Imp has only one original toy. He wants to know if it is possible to use machine to get exactly *x* copied toys and *y* original toys? He can't throw toys away, and he can't apply the machine to a copy if he doesn't currently have any copies.

Input

The only line contains two integers *x* and *y* (0 ≤ *x*, *y* ≤ 10^{9}) — the number of copies and the number of original toys Imp wants to get (including the initial one).

Output

Print "Yes", if the desired configuration is possible, and "No" otherwise.

You can print each letter in arbitrary case (upper or lower).

Examples

Input

6 3

Output

Yes

Input

4 2

Output

No

Input

1000 1001

Output

Yes

Note

In the first example, Imp has to apply the machine twice to original toys and then twice to copies.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Dec/13/2018 03:47:33 (f2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|