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 <iostream>
#include<string>
#include<cmath>
#include<algorithm>
#include<cctype>
#include<queue>
#include<deque>
#include<regex>
#include<stack>
#include<stdio.h>
#include<vector>
#include<set>
#include<map>
#include<iomanip>
#define rep(i,n) for(int i=0;i<n;i++)

typedef int long long ll;
using namespace std;
typedef pair<int,int> P;
int dx[4]={1,0,-1,0};
int dy[4]={0,1,0,-1};
const ll MOD=1e9+7;
static const int MAX = 100;
static const int INF = (1<<23);
template<class T> T gcd(T a, T b){return b? gcd(b,a%b) : a;}
template<class T> T lcm(T a,T b){return a / gcd(a,b)*b;}

int main(){

    int x,y;
    cin>>x>>y;
    if((y-2)%2!=0&&(y-2*x)/2!=0){
        cout<<"No"<<endl;
    }
    int t = x-((y-2)/2);
    int k=(y-2*x)/2;
    if(t>=0&&k>=0){
        cout<<"Yes"<<endl;
    }else{
        cout<<"No"<<endl;
    }

return 0;
}