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.util.*;
import java.io.*;

class Main{
    public static void main(String args[])throws IOException{
        try(BufferedReader br = new BufferedReader(new InputStreamReader(System.in))){
          String[] str = br.readLine().split(" ");
          int X = Integer.parseInt(str[0]);
          int Y = Integer.parseInt(str[1]);

          boolean flag = false;
          int[][] table  = new int[101][101];
          
          for(int i = 0; i <= 100; i++){
            for(int j = 0; j <= 100; j++){
              table[i][j] = i*2 + j*4;
            }
          }

          Loop:for(int i = 0; i <= X; i++){
            for(int j = 0; j <= X; j++){
              if(table[i][j] == Y){
                flag = true;
                break Loop;
              }
            }
          }

          if(flag){
            System.out.println("Yes");
          }else{
            System.out.println("No");
          }
        }

    }
}