Problem: Carl is a beginner magician. He has a blue, b violet and c orange magic spheres. In one move he can transform two spheres of the same color into one sphere of any other color. To make a spell that has never been seen before, he needs at least x blue, y violet and z orange spheres. Can he get them (possible, in multiple actions)?

Input

The first line of the input contains three integers a, b and c (0 ≤ a, b, c ≤ 1 000 000) — the number of blue, violet and orange spheres that are in the magician's disposal.

The second line of the input contains three integers, x, y and z (0 ≤ x, y, z ≤ 1 000 000) — the number of blue, violet and orange spheres that he needs to get.

Output

If the wizard is able to obtain the required numbers of spheres, print "Yes". Otherwise, print "No".

Examples

Input

4 4 0
2 1 2


Output

Yes


Input

5 6 1
2 7 2


Output

No


Input

3 3 3
2 2 2


Output

Yes

Note

In the first sample the wizard has 4 blue and 4 violet spheres. In his first action he can turn two blue spheres into one violet one. After that he will have 2 blue and 5 violet spheres. Then he turns 4 violet spheres into 2 orange spheres and he ends up with 2 blue, 1 violet and 2 orange spheres, which is exactly what he needs.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.StringTokenizer;

public class Main implements Runnable {

    private void solve() throws IOException {
        int a = nextInt();
        int b = nextInt();
        int c = nextInt();

        int x = nextInt();
        int y = nextInt();
        int z = nextInt();

        int delta1 = (x - a) > 0 ? x - a : 0;
        int delta2 = (y - b) > 0 ? y - b : 0;
        int delta3 = (z - c) > 0 ? z - c : 0;

        int need = delta1 + delta2 + delta3;

        int beta1 = (a - x) > 0 ? a - x : 0;
        int beta2 = (b - y) > 0 ? b - y : 0;
        int beta3 = (c - z) > 0 ? c - z : 0;

        int change = beta1 / 2 + beta2 / 2 + beta3 / 2;

        out.println( need > change ? "NO" : "YES");


    }

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

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

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

    String next() throws IOException {
        while (!st.hasMoreTokens()) {
            String line = in.readLine();
            if (line == null)
                return null;
            eat(line);
        }
        return st.nextToken();
    }

    public static void main(String[] args) {
        new Thread(null, new Main(), "Main", 1 << 27).start();
    }

    private BufferedReader in;
    private PrintWriter out;
    private StringTokenizer st;

    String FNAME = "";

    public void run() {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(new OutputStreamWriter(System.out));
            // in = new BufferedReader(new FileReader(FNAME + ".in"));
            // out = new PrintWriter(new FileWriter(FNAME + ".out"));
            // in = new BufferedReader(new FileReader("text.in"));
            // out = new PrintWriter(new FileWriter("text.out"));
            // in = new BufferedReader(new FileReader("input.txt"));
            // out = new PrintWriter(new FileWriter("output.txt"));
            eat("");
            solve();
            in.close();
            out.close();
        } catch (IOException e) {
            e.printStackTrace();
            System.exit(566);
        }
    }

    private void eat(String s) {
        st = new StringTokenizer(s);
    }

}