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>
// #include<iostream>
// #include<vector>
// #include<cmath>
// #include<iomanip>
using namespace std;

const double PI= acos(-1.0);

int gcd_func(int a, int b){
    return b? gcd_func(b, a%b) : a;
} 
 
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    //freopen("in.txt","r",stdin);
    //freopen("out.txt","w",stdout);
    long long x,y; cin >> x >> y;
    long long ns = (y - 2*x)/2;
    if(ns*2 != (y-2*x)){
        cout << "No";
        return 0;
    }
    long long res = ns*4 + (x-ns)*2;
    if(ns < 0 || x - ns < 0){
        cout << "No";
        return 0;
    }
    cout << "Yes";
    return 0;
}