Problem Statement

The time for class reassignment has come again this year.
Every year, the private Yuki High School uses the following algorithm to assign $N$ students to $M$ classes.

　1) Line up the students in order of their grades (from the front: rank $1$, rank $2$, rank $3$, $\dots$ , rank $N$)
　2) Starting from the front of the line, assign $M$ students in order to Class $1$, Class $2$, $\dots$ , Class $M-1$, Class $M$, and remove them from the line. If the end of the line is reached partway through, the process ends there
　3) Assign the next $M$ students in order to Class $M$, Class $M-1$, $\dots$ , Class $2$, Class $1$, and remove them from the line. If the end of the line is reached partway through, the process ends there
　4) Return to 2)

Now, Hanako, a student at Yuki High School, ranked $X$-th out of $N$ students in this school year's grades. Taro, the person Hanako has a crush on, ranked $Y$-th out of $N$ students.
Determine whether Hanako and Taro can be in the same class next school year. Print "$YES$" if they can be in the same class, and "$NO$" if they cannot.
No two people have the same rank in the grade order.

Input

The first line gives the number of students $N$ and the number of classes $M$.
The second line gives Hanako's rank $X$ and Taro's rank $Y$.

$N$ $M$
$X$ $Y$

All input values are integers and satisfy the following constraints.
$2 \leq N \leq 10^9$
$1 \leq M \leq 10^9$
$1 \leq X \leq N$
$1 \leq Y \leq N$
$X \neq Y$

Output

Print "$YES$" if they can be in the same class, and "$NO$" if they cannot. Print a newline at the end.

Sample

10 4
4 5

YES

50 40
50 1

NO

150 7
63 35

YES