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: Wrong Answer)

#include <bits/stdc++.h>
#define F first
#define S second
#define PB push_back
#define MP make_pair
#define all(x) x.begin(), x.end()

using namespace std;

typedef vector<int> vi;
typedef pair<int,int> pi;
typedef vector<pi> vpi;
typedef long long ll;

template <typename T> void max_self(T& a, T b){
  a = max(a,b);
}

template <typename T> void min_self(T& a, T b){
  a = min(a,b);
}

void solve(){	
  int x,y; cin>>x>>y;
  int num = y/4;
  y = y%4;
  if(y%2 == 1 || num > x){
    cout<<"No\n";
  }else if(y == 2 && num+1 > x){
    cout<<"No\n";
  }else{
    cout<<"Yes\n";
  }
}

int main(){
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  //int t; cin >> t;
  //while(t--) solve();
  //
  solve();
  return 0;
}