Problem: Captain Bill the Hummingbird and his crew recieved an interesting challenge offer. Some stranger gave them a map, potion of teleportation and said that only this potion might help them to reach the treasure. 

Bottle with potion has two values x and y written on it. These values define four moves which can be performed using the potion:

  * <image>
  * <image>
  * <image>
  * <image>



Map shows that the position of Captain Bill the Hummingbird is (x1, y1) and the position of the treasure is (x2, y2).

You task is to tell Captain Bill the Hummingbird whether he should accept this challenge or decline. If it is possible for Captain to reach the treasure using the potion then output "YES", otherwise "NO" (without quotes).

The potion can be used infinite amount of times.

Input

The first line contains four integer numbers x1, y1, x2, y2 ( - 105 ≤ x1, y1, x2, y2 ≤ 105) — positions of Captain Bill the Hummingbird and treasure respectively.

The second line contains two integer numbers x, y (1 ≤ x, y ≤ 105) — values on the potion bottle.

Output

Print "YES" if it is possible for Captain to reach the treasure using the potion, otherwise print "NO" (without quotes).

Examples

Input

0 0 0 6
2 3


Output

YES


Input

1 1 3 6
1 5


Output

NO

Note

In the first example there exists such sequence of moves:

  1. <image> — the first type of move 
  2. <image> — the third type of move 

Solution (in JAVA):

Solution:
/* Author: Ronak Agarwal */
import java.io.* ; import java.util.* ; import java.math.* ;
import static java.lang.Math.min ;
import static java.lang.Math.max ;
import static java.lang.Math.abs ;
/* Thread is created here to increase the stack size of the java code so that recursive dfs can be performed */
public class Codeshefcode{
	public static void main(String[] args) throws IOException{
		new Thread(null,new Runnable(){	public void run(){ exec_Code() ;} },"Solver",1l<<27).start() ;
	}
	static void exec_Code(){
		try{
			Solver Machine = new Solver() ;
			Machine.Solve() ; Machine.Finish() ;}
		catch(Exception e){ e.printStackTrace() ; print_and_exit() ;}
		catch(Error e){ e.printStackTrace() ; print_and_exit() ; }
	}
	static void print_and_exit(){ System.out.flush() ; System.exit(-1) ;}
}
/* Implementation of the pair class, useful for every other problem */
class pair implements Comparable<pair>{
	int x ; int y ; int dir ;
	pair(int _x,int _y,int _dir){ x=_x ; y=_y ; dir = _dir ;} 
	public int compareTo(pair p){
		return (this.x<p.x ? -1 : (this.x>p.x ? 1 : (this.y<p.y ? -1 : (this.y>p.y ? 1 : 0)))) ;
	}
}
/* Main code starts here */
class Solver extends Template{
	public void Solve() throws IOException{
		int x1 = ip.i() ; int y1 = ip.i() ;
		x1 = ip.i()-x1 ; 
		y1 = ip.i()-y1 ;
		int x = ip.i() ; int y = ip.i() ;
		if(x1%x!=0 || y1%y!=0){
			pln("NO") ;
			return ;
		}
		x1/=x ; y1/=y ;
		boolean flag = (x1&1) == (y1&1) ;
		pln(flag ? "YES" : "NO") ;
	}
}

/* All the useful functions,constants,renamings are here*/
class Template{
	/* Constants Section */
	final int INT_MIN = Integer.MIN_VALUE ; final int INT_MAX = Integer.MAX_VALUE ;
	final long LONG_MIN = Long.MIN_VALUE ; final long LONG_MAX = Long.MAX_VALUE ;
	static long MOD = 1000000007 ;
	static Reader ip = new Reader(System.in) ;	
	static PrintWriter op = new PrintWriter(System.out) ;
	/* Methods for writing */
	static void p(Object o){ op.print(o) ; }
	static void pln(Object o){ op.println(o) ;}
	static void Finish(){ op.flush();	op.close(); }
	/* Implementation of operations modulo MOD */
	static long inv(long a){ return powM(a,MOD-2) ; }
	static long m(long a,long b){ return (a*b)%MOD ; }
	static long d(long a,long b){ return (a*inv(b))%MOD ; }
	static long powM(long a,long b){
		if(b<0) return powM(inv(a),-b) ;
		long val=a ; long ans=1 ;
		while(b!=0){
			if((b&1)==1) ans = (ans*val)%MOD ; 
			val = (val*val)%MOD ; 
			b/=2 ;
		}
		return ans ;
	}
	/* Renaming of some generic utility classes */
	final static class mylist extends ArrayList<Integer>{}
	final static class myset extends TreeSet<Long>{}
	final static class mystack extends Stack<Integer>{}
	final static class mymap extends TreeMap<Integer,mylist>{}
}

class Reader{
	BufferedReader reader;
	StringTokenizer tkz;
	Reader(InputStream input) {
		reader = new BufferedReader(new InputStreamReader(input)) ;
		tkz = new StringTokenizer("") ;
	}
	String s() throws IOException{
		while (!tkz.hasMoreTokens()) tkz = new StringTokenizer(reader.readLine()) ;
		return tkz.nextToken() ;
	}
	int i() throws IOException{ return Integer.parseInt(s()) ;}
	long l() throws IOException{ return Long.parseLong(s()) ;}
	double d() throws IOException{	return Double.parseDouble(s()) ;}
}