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>
#define ll long long
#define ii pair<int, int>
#define pll pair<ll, ll>
#define N 200123
#define vi vector<int>
#define vii vector<ii>
#define vll vector<ll>
#define vpll vector<pll>
#define pb emplace_back
#define fs first
#define sc second
#define sz(x) ((int)((x).size()))
#define oo 100000012
#define mod 1000000007LL
#define M 10000123

using namespace std;

int f(int a, int b){
    return a*2 + b*4;
}

int main(){
    ios_base::sync_with_stdio(0);

    int n, p;
    cin >> n >> p;

    int ok = 0;
    for(int i = 0; i <= n; ++i){
        for(int j = 0; j <= n; ++j){
            if(i+j == n && f(i, j) == p){
                ok = 1;
                j = n + 1;
                i = n + 1;
            }
        }
    }
    if(ok) cout << "Yes\n";
    else cout << "No\n";
    return 0;
}