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.math.BigInteger;
        import java.text.DecimalFormat;
        import java.util.*;
   
             public class Main {
            	public static InputReader in;
                public static PrintWriter pw;
             
             
             
            	public static void main(String args[]) 
            	{
            		new Thread(null, new Runnable() {
                        public void run() {
                            try{
                                solve();
                            }
                            catch(Exception e){
                                e.printStackTrace();
                            }
                        }
                    }, "1", 1 << 26).start();
                }
            	static ArrayList<Integer> g[];
            	static ArrayList<Integer> h[];
            	static boolean visited[];
            	static int[] parent;
            	static int par[];
            	static int degree[];
            	static int edjes=0;
            	static int start=-1;
            	static int end=-1;
            	static int Total=0;
            	static int time1[];
            	static int time2[];
            	static int glob=0;
            	static int[] ans;
            	static boolean vis2[][];
            	//static long sum1=0;
            	//static long val[];
                static ArrayList<Integer> levels[];
                static int max=0;
                static int lev=1;
                static ArrayList<Integer> nodes[];
                static ArrayList<Integer> values[];
                static int depth[];
                static boolean found=false;
               // static long sm[];
                static int sum1=0;
                static int pre[][];
                static int subtree[];
               static  int cnt=0;
               static  HashMap<String,Integer> hm;
               static int sm[];
               static int size[];
               static long mul[];
               static long d[]=new long[1000000];
               static int tot=0;
               static long highest=(long)1e9;
               static boolean bit=false;
                static Stack<Integer> tt=new Stack();
               static HashSet<Character> set;
         	   static long fact[],num[];
         	   static long MOD=1000000007;
         	   static int value[];static int premen[];
         	   static int count=0,index=0;
         	   static double ans11[];
         	   static int price[];
         	   static ArrayList<String> hp[][];
         	   static boolean visit[][];
         	   static int cnu[]=new int[1000001];
         	   static int label=1;
         	   static int his[][];
         	   static int size1=0;
         	   static int up[],down[];
         	   static int TotalUp=0;
         	   static long dist[];
         	//   static HashMap<String,Integer> hm1=new HashMap();
         	  // static HashMap<Integer,Integer> hm2=new HashMap();
         	   static TreeSet<Long> set1=new TreeSet();
         	  static  long DP[][][]=new long[20][200][1500];
         	 	static int t=-1,n=-1;
         	 	static int two[],min[],r[];
         	 	static int total[];static int black[];
         	 	static int Parent[];
         	 	static int max2[];
         	// 	static int tin[],tout[],a[];
         	 public static void solve() throws FileNotFoundException{
            		
            	
            		 in = new InputReader(System.in);
            		 pw = new PrintWriter(System.out);  
            	/*	 String p=in.readString();
            	     char c[]=p.toCharArray();
            	     int z[]=new int[p.length()];
            	     z[0]=0;
            	     int left=0;
            	     int right=0;
            	     for(int i=1;i<p.length();i++)
            	     {
            	    	 if(i>right)
            	    	 {
            	    		 
            	    		 left=right=i;
            	    		 while(right<p.length()&&c[right]==c[right-left])
            	    			 right++;
            	    		 z[i]=right-left;
            	    		 right--;
            	    	 }
            	    	 else
            	    	 {
            	    		 int k=i-left;
            	    		 if(z[k]<right-i+1)
            	    		 {
            	    			 z[i]=z[k];
            	    		 }
            	    		 else
            	    		 {
            	    			 left=i;
            	    			 while(right<p.length()&&c[right]==c[right-left])
                	    			 right++;
                	    		 z[i]=right-left;
                	    		 right--;
            	    		 }
            	    	 }
            	    	  
            	     }*/
             	   int x1=in.nextInt();
             	    int y1=in.nextInt();
             	    int x2=in.nextInt();
             	    int y2=in.nextInt();
             	    int x=in.nextInt();int y=in.nextInt();
             	    int diff=Math.abs(x1-x2);
             	    if(diff%x!=0)
             	    {
             	    	System.out.println("NO");
             	    	return;
             	    }
             	    int diff1=Math.abs(y1-y2);
             	    if(diff1%y!=0)
             	    {
             	    	System.out.println("NO");
             	    	return;
             	    }
             	    int moveb=(diff1/y);
             	    
             	    int movea=diff/x;
             	    if((moveb-movea)%2==0)
             	    {
             	    	System.out.println("YES");
             	    	return;
             	    }
         	        System.out.println("NO");
         	 }
            
          		public static void bfs(int x)
         	 {
         		 visited[x]=true;
         		 Queue<Integer> Q=new LinkedList<Integer>();
         		 Q.add(x);
         		 while(!Q.isEmpty())
         		 {
         			 int count=Q.size();
         			 while(count>0)
         			 {
         				 int p=Q.poll();
         				 visited[p]=true;
         				 for(int y:g[p])
         				 {
         					 if(!visited[y])
         					 {
         						 Q.add(y);
         					 }
         				 }
         				 count--;
         			 }
         		 }
         	 }
         	 public static void depth(int curr,int parent)
         	 {
         		 visited[curr]=true;
         		 for(int x:g[curr])
         		 {
         			 if(!visited[x])
         			 {
         				 depth[x]=depth[curr]+1;
         				 depth(x,curr);
         			 }
         		 }
         	 }
         	
         	 static int Par[]=new int[202];
         	 public static void Height(int cur,int par){
         		 Par[cur]=par;
         		 visited[cur]=true;
         		 int t=0;
         		 for(int x:g[cur])
         		 {
         			 if(!visited[x])
         			 { 
         				 t++;
         				 Height(x,cur);
         				 high[cur]=Math.max(high[cur], high[x]+1);
         			 }
         		 }
         		 if(t==0)
         		 {
         			 high[cur]=0;
         		 }
         	
         	 }
         	 static int dia[]=new int[202];
         	 static int high[]=new int[292];
         	 public static void Diameter(int curr,int parent)
         	 {
         		visited[curr]=true;
         		int trees=0;
         		ArrayList<Integer> set=new ArrayList();
         	
         		for(int x:g[curr])
         		{
         			if(!visited[x])
         			{
         				trees++;
         				Diameter(x,curr);
         				dia[curr]=Math.max(dia[curr],high[x]);
         				set.add(high[x]);
         			}
         		}
         		if(set.size()>=2)
         		{
         			Collections.sort(set,Collections.reverseOrder());
         			dia[curr]=Math.max(dia[curr],set.get(0)+set.get(1)+2);
         		}
         		else if(set.size()>0)
         		{
         			dia[curr]=Math.max(dia[curr],set.get(0)+1);
         		}
         		if(trees==0)
         		{
         			dia[curr]=0;
         		}
         
         	 }
         	 
              	 
         	 public static boolean IsPal(String s)
         	 {
         		 char c[]=s.toCharArray();
         		 for(int i=0;i<c.length/2;i++)
         		 {
         			 if(c[i]!=c[s.length()-1-i])
         				 return false;
         		 }
         		 return true;
         	 }
         	public static void Merge(long[] a,int p,int r){
                if(p<r){
                    int q = (p+r)/2;
                    Merge(a,p,q);
                    Merge(a,q+1,r);
                    Merge_Array(a,p,q,r);
                }
            }
            public static void Merge_Array(long a[],int p,int q,int r){
               long b[] = new long[q-p+1];
                long c[] = new long[r-q];
                for(int i=0;i<b.length;i++)
                    b[i] = a[p+i];
                for(int i=0;i<c.length;i++)
                    c[i] = a[q+i+1];
                int i = 0,j = 0;
                for(int k=p;k<=r;k++){
                    if(i==b.length){
                        a[k] = c[j];
                        j++;
                    }
                    else if(j==c.length){
                        a[k] = b[i];
                        i++;
                    }
                    else if(b[i]<c[j]){
                        a[k] = b[i];
                        i++;
                    }
                    else{
                        a[k] = c[j];
                        j++;
                    }
                }
            }
         	 
         	 
         	 
         	
         	
               
         	  public static void dfs1(int curr,int parent)
         	  {
         		  visited[curr]=true;
         		  
         		  for(int x:g[curr])
         		  {
         			  
         			  if(x==parent)continue;
         			  depth[x]=depth[curr]+1;
         			  up[x]=up[curr];
         			  if(h[x].contains(curr)){
         				  up[x]++;
         				  TotalUp++;
         			  }
         			  dfs1(x,curr);
         		  }
         	  }
         	 
                
                
                public static void dfs(int curr,int Parent)
                {
                	visited[curr]=true;
                	size[curr]=1;
                	parent[curr]=Parent;
                	count++;
                	if(value[curr]>0)
                	{
                		index=value[curr];
                	}
                	for(int x:g[curr])
                	{
                		if(!visited[x])
                		{
                			dfs(x,curr);
                			size[curr]+=size[x];
                		}
                	}
                }
                static long ncr(long a, long b){
        			if(b>a || b<0) return 0;
        			long f = (fact[(int) a]*modInverse(((fact[(int) b]*fact[(int) (a-b)])%MOD), MOD))%MOD;
        			return f;
        		}
        		static long modInverse(long a, long mOD2){
                    return  power(a, mOD2-2, mOD2);
        }
        static long power(long x, long y, long m)
        {
            if (y == 0)
                return 1;
            long p = power(x, y/2, m) % m;
            p = (p * p) % m;
         
            return (y%2 == 0)? p : (x * p) % m;
        }
         
                public static long gcd(long x, long y) {
            		if (x == 0)
            			return y;
            		else
            			return gcd( y % x,x);
            	}	
                public static long power(long a,long b)
        		{
        			long result=1;
        			while(b>0)
        			{
        				if(b%2==1)
        					result*=a;
        				a=a*a;
        				b/=2;
        			}
        			return result;
        		}
                static class Pair implements Comparable<Pair>{
                	    int l;int r;int ind;
                		Pair(int val,int index,int p){
                	     	this.l=val;
                			this.r=index;
                			this.ind=p;
                		}
                		@Override
                		public int compareTo(Pair o) {
                                 return (l-o.l);
                		}
                				
                	}
            	static class InputReader {
             
            		private InputStream stream;
            		private byte[] buf = new byte[8192];
            		private int curChar, snumChars;
            		private SpaceCharFilter filter;
             
            		public InputReader(InputStream stream) {
            			this.stream = stream;
            		}
             
            		public int snext() {
            			if (snumChars == -1)
            				throw new InputMismatchException();
            			if (curChar >= snumChars) {
            				curChar = 0;
            				try {
            					snumChars = stream.read(buf);
            				} catch (IOException e) {
            					throw new InputMismatchException();
            				}
            				if (snumChars <= 0)
            					return -1;
            			}
            			return buf[curChar++];
            		}
             
            		public   int nextInt() {
            			int c = snext();
            			while (isSpaceChar(c))
            				c = snext();
            			int sgn = 1;
            			if (c == '-') {
            				sgn = -1;
            				c = snext();
            			}
            			int res = 0;
            			do {
            				if (c < '0' || c > '9')
            					throw new InputMismatchException();
            				res *= 10;
            				res += c - '0';
            				c = snext();
            			} while (!isSpaceChar(c));
            			return res * sgn;
            		}
             
            		public long nextLong() {
            			int c = snext();
            			while (isSpaceChar(c))
            				c = snext();
            			int sgn = 1;
            			if (c == '-') {
            				sgn = -1;
            				c = snext();
            			}
            			long res = 0;
            			do {
            				if (c < '0' || c > '9')
            					throw new InputMismatchException();
            				res *= 10;
            				res += c - '0';
            				c = snext();
            			} while (!isSpaceChar(c));
            			return res * sgn;
            		}
             
            		public int[] nextIntArray(int n) {
            			int a[] = new int[n];
            			for (int i = 0; i < n; i++)
            				a[i] = nextInt();
            			return a;
            		}
             
            		public String readString() {
            			int c = snext();
            			while (isSpaceChar(c))
            				c = snext();
            			StringBuilder res = new StringBuilder();
            			do {
            				res.appendCodePoint(c);
            				c = snext();
            			} 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);
            		}
            	}
            }