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.*;

public class Main {

    class IOManager {
        BufferedReader reader;
        PrintWriter writer;
        StringTokenizer tokenizer;

        IOManager() {
            reader = new BufferedReader(new InputStreamReader(System.in));
            writer = new PrintWriter(new BufferedOutputStream(System.out));
        }

        IOManager(String file) throws FileNotFoundException {
            reader = new BufferedReader(new FileReader(file));
            writer = new PrintWriter(new BufferedOutputStream(System.out));
        }

        String next() throws IOException {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                String line = reader.readLine();
                if (line == null)
                    throw new IOException("No lines left.");
                tokenizer = new StringTokenizer(line);
            }
            return tokenizer.nextToken();
        }

        public Integer nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public Long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public Double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public void writeSpace(Object obj) {
            writer.print(obj.toString() + " ");
        }

        public void writeLine(Object obj) {
            writer.println(obj.toString());
        }

        public void writeDouble(Double x, int n) {
            String format = "%." + n + "f";
            writer.printf(format, x);
        }

        public void write(Object obj) {
            writer.print(obj.toString());
        }

        public void close() {
            writer.close();
        }
    }

    class Pair implements Comparable {
        public long u, v;

        public Pair(long u, long v) {
            this.u = u;
            this.v = v;
        }

        @Override
        public int compareTo(Object o) {
            Pair that = (Pair) o;
            if (Long.compare(u, that.u) != 0)
                return Long.compare(u, that.u);
            return Long.compare(v, that.v);
        }
    }

    class Graph {
        public int n, m;
        public List<Integer>[] adj;

        public Graph(int n, int m) {
            this.n = n;
            this.m = m;
            adj = new List[n + 1];
            for (int i = 0; i <= n; ++i) {
                adj[i] = new ArrayList<>();
            }
        }

        public void add(int u, int v) {
            adj[u].add(v);
        }

        public void add2Ways(int u, int v) {
            add(u, v);
            add(v, u);
        }

        public void dfs(int i, boolean fr[]) {
            fr[i] = false;
            for (int j: adj[i]) {
                if (fr[j]) {
                    dfs(j, fr);
                }
            }
        }

        public boolean isConnected() {
            boolean fr[] = new boolean[n + 1];
            Arrays.fill(fr, true);
            dfs(1, fr);
            for (int i = 2; i <= n; ++i) {
                if (fr[i])
                    return false;
            }
            return true;
        }

        public boolean hasEuclideanPath() {
            if (!isConnected())
                return false;
            int cnt = 0;
            for (int i = 1; i <= n; ++i) {
                if (adj[i].size() % 2 == 1)
                    cnt++;
            }
            return cnt <= 2;
        }

        public boolean dfsHamiltonian(int i, boolean[] fr, int reached) {
            fr[i] = false;
            reached++;
            if (reached == n)
                return true;
            for (int j: adj[i]) {
                if (fr[j]) {
                    if (dfsHamiltonian(j, fr, reached))
                        return true;
                }
            }
            fr[i] = true;
            return false;
        }

        public boolean hasHamiltonianPathFrom(int st) {
            boolean fr[] = new boolean[n + 1];
            Arrays.fill(fr, true);
            return dfsHamiltonian(st, fr, 0);
        }
    }

    // Actually rooted forest
    class Tree extends Graph {

        public Tree(int n, int m) {
            super(n, m);
        }

        public int getHeight(int i) {
            int res = 0;
            for (Integer j: adj[i]) {
                res = Math.max(res, getHeight(j) + 1);
            }
            return res;
        }
    }

    class FenwickTree {
        int n;
        int tree[];

        public FenwickTree() {

        }

        public FenwickTree(int maxn) {
            n = maxn;
            tree = new int[maxn + 10];
        }

        public void add(int i, int x) {
            while (i <= n) {
                tree[i] += x;
                i += i & (-i);
            }
        }

        public void add(int i) {
            add(i, 1);
        }

        public int get(int i) {
            int res = 0;
            while (i > 0) {
                res += tree[i];
                i -= i & (-i);
            }
            return res;
        }
    }

    IOManager ioManager;

    Main() {
        ioManager = new IOManager();
    }

    Main(String file) throws FileNotFoundException {
        ioManager = new IOManager(file);
    }

    void solve() throws IOException {
        long x1, y1, x2, y2;
        x1 = ioManager.nextLong();
        y1 = ioManager.nextLong();
        x2 = ioManager.nextLong();
        y2 = ioManager.nextLong();
        long x, y;
        x = ioManager.nextLong();
        y = ioManager.nextLong();
        long dx = Math.abs(x2 - x1);
        long dy = Math.abs(y2 - y1);
        if (dx % x != 0 || dy % y != 0) {
            ioManager.writeLine("NO");
            return;
        }
        long kx = dx / x, ky = dy / y;
        if ((kx + ky) % 2 == 1) {
            ioManager.writeLine("NO");
            return;
        }
        ioManager.writeLine("YES");
    }

    void close() {
        ioManager.close();
    }

    public static void main(String args[]) throws IOException {
        Main solver;
        if (!"true".equals(System.getProperty("ONLINE_JUDGE"))) {
            solver = new Main("input.txt");
        } else {
            solver = new Main();
        }
        solver.solve();
        solver.close();
    }
}