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.*;
import java.util.*;
import java.lang.Math;
import java.math.BigInteger;

public class Problem {

	public static void main(String[] args) throws IOException {

		new Problem().run();
	}
//
	BufferedReader in;
	PrintWriter out;
	StringTokenizer tok;
	Random rnd = new Random();
	static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
	Problem() throws FileNotFoundException{

		if (ONLINE_JUDGE) {
			in = new BufferedReader(new InputStreamReader(System.in)); 
            out = new PrintWriter(System.out); 
		} else {
			in = new BufferedReader(new FileReader("input.txt"));
			out = new PrintWriter("output.txt");
		}
		tok = new StringTokenizer("");
	}

	// ======================================================
	
	class Dsu{
		int[] parents;
		int countUnions;
		Dsu(int size){
			this.parents = new int[size];
			this.countUnions = size;
			for(int i=0;i<size;++i){
				parents[i] = i;
			}
		}
		int get(int v){
			if(v == parents[v]){
				return v;
			}
			return parents[v] = get(parents[v]);
		}
		boolean union(int a, int b){
			if(parents[a]==parents[b]) return false;
			if(rnd.nextBoolean()){
				parents[a] = b;
			}else{
				parents[b] = a;
			}
			countUnions--;
			return true;
		}
	}
	int INF = 1000*1000*1000+7;
	void solve() throws IOException {
		int x1 = rI();
		int y1 = rI();
		int x2 = rI();
		int y2 = rI();
		int x = rI();
		int y = rI();
		
		if(Math.abs(x1-x2)%x==0&&(Math.abs(y1-y2)%y==0)&&(Math.abs(x1-x2)/x-(Math.abs(y1-y2))/y)%2==0){
			out.println("YES");
		}else{
			out.println("NO");
		}
		
	}	

	// ======================================================
	void run() throws IOException {
		solve();
		out.close();
	}

	char[] reverseCharArray(char[] arr){
		char[] ans = new char[arr.length];
		for(int i=0;i<arr.length;++i){
			ans[i] = arr[arr.length-i-1];
		}
		return ans;
	}
	int sqrt(double m){
		int l = 0;
		int r = 1000000000+9;
		int i=1000;
		while(r-l>1){
			int mid = (r+l)/2;
			if(mid*mid>m){
				r = mid;
			}else{
				l = mid;
			}
		}
		return l;
	}
	int countPow(int m,int n){
		int ans = 0;
		while(m%n==0&&m>0){
			ans++;
			m/=n;
		}
		return ans;
	}
	long binPow(long a, long b){
		if(b == 0){
			return 1;
		}
		if(b%2==1){
			return a*binPow(a,b-1);
		}else{
			long c = binPow(a,b/2);
			return c*c;
		}
		
	}
	long gcd(long a, long b){
		return b==0?a:gcd(b,a%b);
	}
	
	long pow(long x, long k){
		long ans=1;
		for(int i=0;i<k;++i){
			ans*=x;
		}
		return ans;
	}
	//////////////////////////////////////////////////////////////////////


	String delimiter = " ";
	String readLine() throws IOException {
		return in.readLine();
	}
	String rS() throws IOException {
		while (!tok.hasMoreTokens()) {
			String nextLine = readLine();
			if (null == nextLine)
				return null;

			tok = new StringTokenizer(nextLine);
		}

		return tok.nextToken(delimiter);
	}
	int rI() throws IOException {
		return Integer.parseInt(rS());
	}

	long rL() throws IOException {
		return Long.parseLong(rS());
	}
	int[] rA(int b) {
		int a[] = new int[b];
		for (int i = 0; i < b; i++) {
			try {
				a[i] = rI();
			} catch (IOException e) {
				e.printStackTrace();
			}
		}
		return a;
	}
	
	int[] readSortedIntArray(int size) throws IOException {
	        Integer[] array = new Integer[size];

	        for (int index = 0; index < size; ++index) {
	            array[index] = rI();
	        }
	        Arrays.sort(array);

	        int[] sortedArray = new int[size];
	        for (int index = 0; index < size; ++index) {
	            sortedArray[index] = array[index];
	        }

	        return sortedArray;
	    }

}