Problem:
Score : 200 points

Problem Statement

There are some animals in a garden. Each of them is a crane with two legs or a turtle with four legs.

Takahashi says: "there are X animals in total in the garden, and they have Y legs in total." Determine whether there is a combination of numbers of cranes and turtles in which this statement is correct.

Constraints

1 \leq X \leq 100

1 \leq Y \leq 100

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y

Output

If there is a combination of numbers of cranes and turtles in which the statement is correct, print Yes; otherwise, print No.

Sample Input 1

3 8

Sample Output 1

Yes

The statement "there are 3 animals in total in the garden, and they have 8 legs in total" is correct if there are two cranes and one turtle. Thus, there is a combination of numbers of cranes and turtles in which the statement is correct.

Sample Input 2

2 100

Sample Output 2

No

There is no combination of numbers of cranes and turtles in which this statement is correct.

Sample Input 3

1 2

Sample Output 3

Yes

We also consider the case in which there are only cranes or only turtles.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.UncheckedIOException;
import java.util.ArrayDeque;
import java.util.Deque;
import java.util.regex.Pattern;

public class Main {
    public void exec(Stdin stdin, PrintWriter stdout) {
        int x = stdin.nextInt();
        int y = stdin.nextInt();
        if (4*x-y>0 && (4*x-y)%2==0) {
            stdout.println("Yes");
        } else {
            stdout.println("No");
        }
    }

    public static void main(String[] args) {
        Stdin stdin = new Stdin();
        PrintWriter stdout = new PrintWriter(System.out, false);
        new Main().exec(stdin, stdout);
        stdout.flush();
    }


    public static class Stdin {
        private BufferedReader stdin;
        private Deque<String> tokens;
        private Pattern delim;

        public Stdin() {
            stdin = new BufferedReader(new InputStreamReader(System.in));
            tokens = new ArrayDeque<>();
            delim = Pattern.compile(" ");
        }

        public String nextString() {
            try {
                if (tokens.isEmpty()) {
                    String line = stdin.readLine();
                    delim.splitAsStream(line).forEach(tokens::addLast);
                }
                return tokens.pollFirst();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public int nextInt() {
            return Integer.parseInt(nextString());
        }

        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }
    }
}