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. Triangle

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere is a right triangle with legs of length *a* and *b*. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.

Input

The first line contains two integers *a*, *b* (1 ≤ *a*, *b* ≤ 1000), separated by a single space.

Output

In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers — the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 10^{9} in their absolute value.

Examples

Input

1 1

Output

NO

Input

5 5

Output

YES

2 1

5 5

-2 4

Input

5 10

Output

YES

-10 4

-2 -2

1 2

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/30/2017 23:25:36 (p1).

Desktop version, switch to mobile version.
User lists

Name |
---|