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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

int main(){
  
  int a,b,c;
  bool answer = false;
  cin >> a >> b;
  
  c = 2*a;
  
  vector<int> vec(a+1);
  for(int i=0;i<a+1;i++){
    
    c += 2;
  
  if( b == c ){
    
    answer = true;
    
  }
    
  else if( b == 2*a ){
    
    answer = true;
    
  }
    
  }
    
  if( b == 4*a +2 ){
    
    answer = false;
    
  }
    
  if( answer ){
    
    cout << "Yes" << endl;
    
  }
    
  else{
    
    cout << "No" << endl;
    
  }
    
}