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 <iostream>
#include <string>
#include <sstream>
#include <utility>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <queue>
#include <cmath>
#include <functional>
#include <chrono>
#include <cstring>
#include <limits.h>

using namespace std;
typedef long long lint;
typedef vector<int> vi;
typedef pair<int,int> pii;
typedef vector<lint> vl;
typedef pair<lint,lint> pll;

int main()
{
    ios_base::sync_with_stdio(0);    cin.tie(NULL);    cout.tie(NULL);

    int x, y; cin>>x>>y;

    int turleg = y - 2*x;
    if (turleg >= 0 && turleg%2 == 0 && turleg/2 <= x) cout<<"Yes";
    else cout<<"No";

}