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;

typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef vector<string> vs;
typedef pair<int, int> P;

#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()

void YN(bool flg){if(flg) cout << "YES" << endl; else cout << "NO" << endl;}
void Yn(bool flg){if(flg) cout << "Yes" << endl; else cout << "No" << endl;}
void yn(bool flg){if(flg) cout << "yes" << endl; else cout << "no" << endl;}

int main()
{
    int x, y;
    cin >> x >> y;
    bool flg = false;
    rep(i, x+1) {
        rep(j, x+1) {
            if(i + j != x) continue;
            if(i*2 + j*4 == y) flg = true;
        }
    }
    Yn(flg);

    return 0;
}