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.util.*;
import java.io.*;
import java.lang.*;
import java.math.*;

public class cf1 {
	 static class pair implements Comparable<pair>
		{
			Integer x,y;
			pair(int x,int y)
			{
				this.x=x;
				this.y=y;
			}
			public int compareTo(pair o) {
				if(y!=o.y)
					return y.compareTo(o.y);
				else
					return x.compareTo(o.x);
			}  
		}
	static long mod=1000000007;
	static boolean prime[];
	public static void main(String args[])
	{
		InputReader in=new InputReader(System.in);
		PrintWriter pw=new PrintWriter(System.out);
		int x1=in.nextInt();
		int y1=in.nextInt();
		int x2=in.nextInt();
		int y2=in.nextInt();
		int x=in.nextInt();
		int y=in.nextInt();
		boolean flag=true;
		while(true)
		{
			if(x1==x2 && y1==y2)
				break;
			if(x1==x2 && y1<y2)
			{
				while(y1<y2)
				{
					x1=x1+x;
					y1=y1+y;
					x1=x1-x;
					y1=y1+y;
				}
				if(y1==y2)
					break;
				else
				{
					flag=false;
					break;
				}
			}
			if(x1==x2 && y1>y2)
			{
				while(y1>y2)
				{
					x1=x1+x;
					y1=y1-y;
					x1=x1-x;
					y1=y1-y;
				}
				if(y1==y2)
					break;
				else
				{
					flag=false;
					break;
				}
			}
			if(x1<x2 && y1==y2)
			{
				while(x1<x2)
				{
					x1=x1+x;
					y1=y1+y;
					x1=x1+x;
					y1=y1-y;
				}
				if(x1==x2)
					break;
				else
				{
					flag=false;
					break;
				}
			}
			if(x1>x2 && y1==y2)
			{
				while(x1>x2)
				{
					x1=x1-x;
					y1=y1+y;
					x1=x1-x;
					y1=y1-y;
				}
				if(x1==x2)
					break;
				else
				{
					flag=false;
					break;
				}
			}
			if(x1<x2 && y1<y2)
			{
				while(x1<x2 && y1<y2)
				{
					x1=x1+x;
					y1=y1+y;
				}
				if(x1==x2 || y1==y2)
					continue;
				else
				{
					flag=false;
					break;
				}
			}
			if(x1<x2 && y1>y2)
			{
				while(x1<x2 && y1>y2)
				{
					x1=x1+x;
					y1=y1-y;
				}
				if(x1==x2 || y1==y2)
					continue;
				else
				{
					flag=false;
					break;
				}
			}
			if(x1>x2 && y1<y2)
			{
				while(x1>x2 && y1<y2)
				{
					x1=x1-x;
					y1=y1+y;
				}
				if(x1==x2 || y1==y2)
					continue;
				else
				{
					flag=false;
					break;
				}
			}
			if(x1<x2 && y1>y2)
			{
				while(x1<x2 && y1>y2)
				{
					x1=x1+x;
					y1=y1-y;
				}
				if(x1==x2 || y1==y2)
					continue;
				else
				{
					flag=false;
					break;
				}
			}
			if(x1<x2 && y1>y2)
			{
				while(x1<x2 && y1>y2)
				{
					x1=x1+x;
					y1=y1-y;
				}
				if(x1==x2 || y1==y2)
					continue;
				else
				{
					flag=false;
					break;
				}
			}
			if(x1>x2 && y1>y2)
			{
				while(x1>x2 && y1>y2)
				{
					x1=x1-x;
					y1=y1-y;
				}
				if(x1==x2 || y1==y2)
					continue;
				else
				{
					flag=false;
					break;
				}
			}
		}
		if(flag)
			pw.print("Yes");
		else
			pw.println("No");
		pw.flush();
	}
	public static int distance(int x,int y,int p,int q)
	{
		int a=(x-p)*(x-p);
		int b=(y-q)*(y-q);
		int dis=a+b;
		return dis;
	}
	public static int bnum(int num)
	{
		int ans=0;
		for(int i=31;i>=0;i--)
		{
			if((num&(1<<i))!=0)
			{
				ans+=Math.pow(10,i);
			}
		}
		return ans;
	}
	public static int bsdown(int a[],int item)
	{
		int low=0,high=a.length-1,ans=-1;
		while(low<=high)
		{
			int mid=low+(high-low)/2;
			if(a[mid]<=item)
			{
				ans=mid;
				low=mid+1;
			}
			else
				high=mid-1;
				
		}
		return ans;
	}
	public static long inverse(long num)
	{
		return fastpow(num,mod-2,mod);
	}
	public static int bsupper(int a[],int item)
	{
		int low=0,high=a.length-1,ans=-1;
		while(low<=high)
		{
			int mid=low+(high-low)/2;
			if(a[mid]>=item)
			{
				ans=mid;
				high=mid-1;
			}
			else
				low=mid+1;
				
		}
		return ans;
	}	
	public static boolean isprime(int n)
	{
		for(int i=2;i*i<=n;i++)
		{
			if(n%i==0)
				return false;
		}
		return true;
	}
	public static long fact(long a,long mod)
	{
		long ans=1;
		for(int i=1;i<=a;i++)
		{
			ans*=i;
			ans%=mod;
		}
		return ans%mod;
		
	}
	public static long ncr(long n,long r,long mod)
	{
		long nom=1,dom=1;
		nom=(fact(n,mod))%mod;
		dom=(fact(r,mod)*fact(n-r,mod))%mod;
		return (nom*fastpow(dom,mod-2,mod))%mod;
	}
	public static long gcd(long x, long y)
	{
		if(x==0)
			return y;
		if(y==0)
			return x;
		long r=0, a, b;
		a = (x > y) ? x : y; // a is greater number
		b = (x < y) ? x : y; // b is smaller number
		r = b;
		while(a % b != 0)
		{
			r = a % b;
			a = b;
			b = r;
		}
		return r;
	}
	public static void prime(int n)
	{
		prime[0]=true;
		prime[1]=true;
		for(int i=2;i*i<=n;i++)
		{
			if(prime[i])
				continue;
			for(int j=i;j*i<=n;j++)
			{
				prime[i*j]=true;
			}
		}
	}
	static class InputReader {
		 
		private final InputStream stream;
		private final 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 String nextLine() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isEndOfLine(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;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
	public static long fastpow(long a,long b,long mod)
	{
		long ans=1;
		while(b!=0)
		{
			if(b%2==1)
			{
				ans=(ans*a)%mod;
			}
			a=(a*a)%mod;
			b/=2;
		}
		return ans;
	}
}