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:
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.Iterator;


public class Main
{
    static class Pair{
    	int first,second;
    	public Pair(int first,int second){
    		this.first=first;
    		this.second=second;
    	}
    }
	//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
	static class Solution
	{
		final long mod = 1000000007;
		final int  max = (int)1e6+2;
		
		////////////////////////////////
		

	    public void solve(InputReader sc,PrintWriter out) 
	    {
	        
	            int x1=i(),y1=i(),x2=i(),y2=i();
	            int x=i(),y=i();
	            int dx = Math.abs(x1-x2);
	            int dy = Math.abs(y1-y2);

	            if(dx%x==0 && dy%y==0)
	            {
	            	if((dx/x)%2==(dy/y)%2)
	            		out.println("YES");
	            	else
	            		out.println("NO");
	            }
	            else
	            	out.println("NO");
	        
		         
	      
    	}
       	
    	///////////////////////////////Methods///////////////////////////////////////////////////////
        int lower_bound(ArrayList<Integer> a, int key) {
    		int l = 0;
    		int h = a.size(); // Not n - 1

    		
    		
    		while (l < h) {
        		int mid = (l + h) / 2;
        		if (key <= a.get(mid)) {
            		h = mid;
        		} else {
            		l = mid + 1;
        		}
    		}
    		return l;
		}
    	int upper_bound(ArrayList<Integer> a, int key) {
    		int l = 0;
   		    int h = a.size(); // Not n - 1

   		    if(key>=a.get(h-1))
    			return (h);
    		
   			while (l < h) {
        		int mid = (l + h) / 2;
        		if (key >= a.get(mid)) {
            		l = mid + 1;
        		} else {
            		h = mid;
        		}
    		}
	
    		return l;
		}

        ////////////////////////////////////////////////////////////
        public int i(){	return sc.nextInt();}
		public long l(){ return sc.nextLong();}
		public String s(){ return sc.next();}
		public int[] iarr(int n){int[] ar = new int[n];for(int i=0;i<n;++i) ar[i] = sc.nextInt(); return ar; }
		public long[] larr(int n){long[] ar = new long[n+1];for(int i=1;i<=n;++i) ar[i] = sc.nextLong(); return ar; }
		public void parr(int[] ar){	for(int i=0;i<ar.length;i++)	out.print(ar[i]+" ");
			out.println();
		}
		public void parl(long[] ar){	for(int i=0;i<ar.length;i++)	out.print(ar[i]+" ");
			out.println();
		}
        ///////////////////////////////////////Methods/////////////////////////////////////////////////////
 	}
    

 	////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 	static	InputReader sc = new InputReader();
	static    PrintWriter out= new PrintWriter(System.out);
	Main() throws IOException {
	   
	    final long start = System.currentTimeMillis();		
		new Solution().solve(sc,out);
		@SuppressWarnings("unused")
		final long duration = System.currentTimeMillis()-start;
		out.close();
	}
 
	public static void main(String args[]) {
		new Thread(null, new Runnable() {
			public void run() {
				try {
					new Main();
				} catch (Exception e) {
					e.printStackTrace();
				}
			}
		}, "1", 1 << 26).start();
	}
	static class InputReader{
		final InputStream stream;
		final byte[] buf = new byte[8192];
		int curChar, numChars;
		SpaceCharFilter filter;
 
		public InputReader(){
			this.stream = System.in;
		}
 
		public int read(){
			if(numChars == -1){
				throw new InputMismatchException();
			}
			if(curChar >= numChars){
				curChar = 0;
				try{
					numChars = stream.read(buf);
				} catch(IOException e){
					throw new InputMismatchException();
				}
				if(numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
 
		public int nextInt(){
			int c = read();
			while(isSpaceChar(c))
				c = read();
			int sgn = 1;
			if(c == '-'){
				sgn = -1;
				c = read();
			}
			int res = 0;
			do{
				if(c<'0' || c>'9'){
					throw new InputMismatchException();}
				res *= 10;
				res += c - '0';
				c = read();
			} while(!isSpaceChar(c));
			return res*sgn;
		}
 
		public long nextLong(){
			int c = read();
			while(isSpaceChar(c))
				c = read();
			int sgn = 1;
			if(c == '-'){
				sgn = -1;
				c = read();
			}
			long res = 0;
			do{
				if(c<'0' || c>'9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while(!isSpaceChar(c));
			return res*sgn;
		}
 
		public String next(){
			int c = read();
			while(isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do{
				res.appendCodePoint(c);
				c = read();
			}while(!isSpaceChar(c));
			return res.toString();
		}
 
		public boolean isSpaceChar(int c){
			if(filter != null)
				return filter.isSpaceChar(c);
			return c==' ' || c=='\n' || c=='\r' || c=='\t' || c==-1;
		}
 
		public interface SpaceCharFilter{
			public boolean isSpaceChar(int ch);
		}
	}

}