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;

#define rep(i, a) for (int i = 0; i < (a); i++ )
#define FOR(i, m, n) for(int i = m; i < n; i++)
 
typedef pair<int,int> P;
typedef long long ll;
 
const int INF = 1001001001;
const int MOD = 1000000007;
const double PI=acos(-1);

int main(){
    int X,Y;
    cin >> X >> Y;
    string ans = "No";  
    rep(k,X+1) {
        int t = X-k;
        int s = 4*k+2*t;
        if (s==Y) {
            ans = "Yes";
        }
    }
    cout << ans << endl;
}