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: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

#define int 		long long
#define endl		"\n"
#define mod			1000000007
#define IOS			ios::sync_with_stdio(0), cin.tie(0), cout.tie(0)

int32_t main() {

	IOS;

	int x, y, c = 0, t;
	cin >> x >> y;
	bool valid = false;

	t = x;

	while (t >= 0) {
		if ( t * 4 + c * 2 == y) {
			valid = true;
			break;
		}
		else
			t--, c++;
	}

	if (valid)
		cout << "YES\n";
	else
		cout << "NO\n";

	return 0;
}