Petryk and the exam

Today Petrik finally took the exam in mathematical analysis. The exam had $a$ easy problems and $b$ difficult ones, and each difficult problem was worth twice as many points as an easy problem.

Petrik remembers that he could not solve exactly $x$ easy and $y$ hard problems, but he solved all other problems correctly.

Now Petrik is wondering whether he should be happy about passing the exam if to pass, he needs to get at least $51\%$ of the maximum possible score.

Note that if Petrik scores exactly $50.5\%$ of the maximum score, then the exam is considered failed.

Input

The first line contains four integers $a$, $b$, $x$, and $y$ ($1\le x\le a\le 10^5,1\le y\le b\le 10^5$).

Output

If Petrik passed the exam, output «YES»; otherwise, output «NO». The output can be in any case.

Examples

Note

In the first example, Petrik could not solve any problems, so he failed the exam.

In the second example, Petrik did not solve $3$ out of $12$ easy problems and $2$ out of $4$ difficult ones. This means that he solved $9$ out of $12$ easy problems and $2$ out of $4$ difficult ones correctly. If each easy problem is worth $c$ points, then Petrik got $9c$ points for the easy problems and $2\cdot 2c$ points for the difficult problems, giving a total of $13c$ points. The maximum possible score is $12c+2\cdot 4c=20c$ points, so when we calculate his result as a percentage of the maximum possible score, we get $65\%$, which is greater than $51\%$.

In the third example, Petrik did not solve $2$ out of $5$ easy problems and $2$ out of $3$ difficult ones. This means that he solved $3$ out of $5$ easy problems and $1$ out of $3$ difficult ones correctly. If each easy problem is worth $c$ points, then Petrik got $3c$ points for the easy problems and $2\cdot 1c$ points for the difficult problems, giving a total of $5c$ points. The maximum possible score is $5c+2\cdot 3c=11c$ points, so when we calculate his result as a percentage of the maximum possible score, we get approximately $45\%$, which is less than $51\%$.