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. Infinite Sequence

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVasya likes everything infinite. Now he is studying the properties of a sequence *s*, such that its first element is equal to *a* (*s*_{1} = *a*), and the difference between any two neighbouring elements is equal to *c* (*s*_{i} - *s*_{i - 1} = *c*). In particular, Vasya wonders if his favourite integer *b* appears in this sequence, that is, there exists a positive integer *i*, such that *s*_{i} = *b*. Of course, you are the person he asks for a help.

Input

The first line of the input contain three integers *a*, *b* and *c* ( - 10^{9} ≤ *a*, *b*, *c* ≤ 10^{9}) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.

Output

If *b* appears in the sequence *s* print "YES" (without quotes), otherwise print "NO" (without quotes).

Examples

Input

1 7 3

Output

YES

Input

10 10 0

Output

YES

Input

1 -4 5

Output

NO

Input

0 60 50

Output

NO

Note

In the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.

In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.

In the third sample all elements of the sequence are greater than Vasya's favorite integer.

In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Dec/18/2018 19:18:46 (f1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|