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:
/*
 * DA-IICT
 * Author: Jugal Kalal
 */
import java.util.*;
import java.io.*;
import java.math.*;
import java.text.DecimalFormat;
public class HackerEarth{
	static long MOD=(long)Math.pow(10,9)+7;
	public static void main(String args[]) {
        new Thread(null, new Runnable() {
            public void run() {
                try{
                    solve();
                    w.close();
                }
                catch(Exception e){
                    e.printStackTrace();
                }
            }
        }, "1", 1 << 26).start();
	}
	static InputReader in;
    static PrintWriter w;
    static void solve(){
        in = new InputReader(System.in);
        w = new PrintWriter(System.out);
        int x1=in.nextInt();
        int y1=in.nextInt();
        int x2=in.nextInt();
        int y2=in.nextInt();
        int a=in.nextInt();
        int b=in.nextInt();
        double num1=((double)(x2-x1))/(double)a;
        double num2=((double)(y2-y1))/(double)b;
        long ln1=(long)num1;
        long ln2=(long)num2;
        if(((double)ln1!=num1||(double)ln2!=num2)){
        	w.println("NO");
        	return;
        }
        long jack=(long)Math.abs(ln1-ln2);
        if(jack%2l==0){
        	w.println("YES");
        }else{
        	w.println("NO");
        }
    }
    static boolean adj[][];
//    static ArrayList<Integer> adj[]; //Adjacency Lists
    static int V;   // No. of vertices
    // Constructor
    static void Graph(int v){
        V = v;
        adj=new boolean[v][v];
//        adj = new ArrayList[v];
//        for (int i=0; i<v; ++i){
//        	adj[i] = new ArrayList();
//        }
    }
    // Function to add an edge into the graph
    static void addEdge(int u,int v){
//		adj[u].add(v);
//		adj[v].add(u);
    	adj[u][v]=true;
    	adj[v][u]=true;
    }
    static int[] isHamiltonian_path(int n){
    	int ans[]=new int[n];
    	int dp[][]=new int[n][1<<n];
    	for(int i=0;i<n;i++){
    		dp[i][1<<i]=0;
    	}
    	for(int mask=0;mask<(1<<n);mask++){
    		for(int j=0;j<n;j++){
    			if((mask&(1<<j))>0){
    				for(int k=0;k<n;k++){
    					if(j!=k&&(mask&(1<<k))>0&&adj[j][k]){
    						dp[j][mask]=Math.max(1+dp[k][mask^(1<<j)],dp[j][mask]);
    					}
    				}
    			}
    		}
    	}
    	for(int i=0;i<n;i++){
    		ans[i]=dp[i][(1<<n)-1];
    	}
    	return ans;
    }
//    static void bfs(int s,int n){
//    	boolean visited[]=new boolean[n];
//    	LinkedList<Integer> queue=new LinkedList<Integer>();
//    	queue.add(s);
//    	visited[s]=true;
//    	while(!queue.isEmpty()){
//    		int num=queue.pop();
////    		System.out.println(ans.toString());
//    		for(int i=0;i<adj[num].size();i++){
//    			if(!visited[adj[num].get(i)]){
//    				visited[adj[num].get(i)]=true;
//    				queue.add(adj[num].get(i));
//    			}
//    		}
//    	}
//    }
    static long gcd(long a,long b){
		if(a==0){
			return b;
		}
		return gcd(b%a,a);
	}
    static long power(long base, long exponent, long modulus){
	    long result = 1L;
	    while (exponent > 0) {
	        if (exponent % 2L == 1L)
	            result = (result * base) % modulus;
	        exponent = exponent >> 1;
	        base = (base * base) % modulus;
	    }
	    return result;
	}
    static HashMap<Long,Long> primeFactors(long n){
        HashMap<Long,Long> ans=new HashMap<Long,Long>();
    	// Print the number of 2s that divide n
        while (n%2L==0L)
        {
            if(ans.containsKey(2L)){
            	ans.put(2L,ans.get(2L)+1L);
            }else{
            	ans.put(2L,1L);
            }
            n /= 2L;
        }
 
        // n must be odd at this point.  So we can
        // skip one element (Note i = i +2)
        for (long i = 3; i <= Math.sqrt(n); i+= 2L)
        {
            // While i divides n, print i and divide n
            while (n%i == 0)
            {
            	if(ans.containsKey(i)){
                	ans.put(i,ans.get(i)+1L);
                }else{
                	ans.put(i,1L);
                }
                n /= i;
            }
        }
 
        // This condition is to handle the case whien
        // n is a prime number greater than 2
        if (n > 2)
            ans.put(n,1L);
        return ans;
    }
////for marking all prime numbers greater than 1 and less than equal to N
	static void sieve(int N) {
	 boolean isPrime[]=new boolean[N+1];
	 isPrime[0] = true;
	 isPrime[1] = true;
	 for(int i = 2; i * i <= N; ++i) {
	      if(isPrime[i] == false) {//Mark all the multiples of i as composite numbers
	          for(int j = i * i; j <= N ;j += i)
	              isPrime[j] = true;
	     }
	 }
	}
//  //if  str2 (pattern) is subsequence of str1 (Text) or not
//	static boolean function(String str1,String str2){
//	     str2 = str2.replace("", ".*");  //returns .*a.*n.*n.*a.
//	     return (str1.matches(str2));  // returns true
//	}
    static int Arr[];
    static long size[];
  //modified initialize function:
    static void initialize(int N){
    	Arr=new int[N];
    	size=new long[N];
        for(int i = 0;i<N;i++){
        	Arr[ i ] = i ;
        	size[ i ] = 1;
        }
    }
    static boolean find(int A,int B){
        if( root(A)==root(B) )       //if A and B have same root,means they are connected.
        return true;
        else
        return false;
    }
 // modified root function.
    static void weighted_union(int A,int B,int n){
        int root_A = root(A);
        int root_B = root(B);
        if(size[root_A] < size[root_B ]){
        	Arr[ root_A ] = Arr[root_B];
        	size[root_B] += size[root_A];
        }
        else{
        	Arr[ root_B ] = Arr[root_A];
        	size[root_A] += size[root_B];
        }
    }
    static int root (int i){
        while(Arr[ i ] != i){
            Arr[ i ] = Arr[ Arr[ i ] ] ; 
            i = Arr[ i ]; 
        }
        return i;
    }
    
 
	static boolean isPrime(long n) {
		if(n < 2L) return false;
		if(n == 2L || n == 3L) return true;
		if(n%2L == 0 || n%3L == 0) return false;	
		long sqrtN = (long)Math.sqrt(n)+1L;
		for(long i = 6L; i <= sqrtN; i += 6L) {
			if(n%(i-1) == 0 || n%(i+1) == 0) return false;
		}
		return true;
	}
//	static HashMap<Integer,Integer> level;;
//	static HashMap<Integer,Integer> parent;
	static int maxlevel=0;
	
//	static boolean T[][][];
//	static void subsetSum(int input[], int total, int count) {
//        T = new boolean[input.length + 1][total + 1][count+1];
//        for (int i = 0; i <= input.length; i++) {
//        	T[i][0][0] = true;
//        	for(int j = 1; j<=count; j++){
//        		T[i][0][j] = false;
//        	}
//        }
//        int sum[]=new int[input.length+1];
//        for(int i=1;i<=input.length;i++){
//            sum[i]=sum[i-1]+input[i-1];
//        }
//        for (int i = 1; i <= input.length; i++) {
//            for (int j = 1; j <= (int)Math.min(total,sum[i]); j++) {
//            	for (int k = 1; k <= (int)Math.min(i,count); k++){
//            		 if (j >= input[i - 1]) {//Exclude and Include
//                         T[i][j][k] = T[i - 1][j][k] || T[i - 1][j - input[i - 1]][k-1];
//                     } else {
//                         T[i][j][k] = T[i-1][j][k];
//                     }
//            	}
//            }
//        }
//    }
//	static <K,V extends Comparable<? super V>>
//	SortedSet<Map.Entry<K,V>> entriesSortedByValues(Map<K,V> map) {
//	    SortedSet<Map.Entry<K,V>> sortedEntries = new TreeSet<Map.Entry<K,V>>(
//	        new Comparator<Map.Entry<K,V>>() {
//	            @Override public int compare(Map.Entry<K,V> e1, Map.Entry<K,V> e2) {
//	                int res = e2.getValue().compareTo(e1.getValue());
//	                return res != 0 ? res : 1;
//	            }
//	        }
//	    );
//	    sortedEntries.addAll(map.entrySet());
//	    return sortedEntries;
//	}
	
 
	 
	//minimum prime factor of all the numbers less than n
    static int minPrime[];
	static void minimumPrime(int n){
		minPrime=new int[n+1];
		minPrime[1]=1;
        for (int i = 2; i * i <= n; ++i) {
            if (minPrime[i] == 0) {         //If i is prime
                for (int j = i * i; j <= n; j += i) {
                    if (minPrime[j] == 0) {
                        minPrime[j] = i;
                    }
                }
            }
        }
        for (int i = 2; i <= n; ++i) {
            if (minPrime[i] == 0) {
                minPrime[i] = i;
            }
        }
	}
	static long modInverse(long A, long M)
	{
		long x=extendedEuclid(A,M)[0];
		return (x%M+M)%M;    //x may be negative
	}
	static long[] extendedEuclid(long A, long B) {
		if(B == 0) {
			long d = A;
			long x = 1;
			long y = 0;
			return new long[]{x,y,d};
		}
		else {
			long arr[]=extendedEuclid(B, A%B);
			long temp = arr[0];
			arr[0] = arr[1];
			arr[1] = temp - (A/B)*arr[1];
			return arr;
		}
	}
 
	static class InputReader {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, numChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
        
        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 String nextLine() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        public String readString() {
            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 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 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 int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }
 
        public long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }
 
        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
	}
}