Problem Statement

There is a grid of $H$ rows $×W$ columns.
People numbered $1$ to $N$ take turns in order, starting with person $1$; on each turn, a person chooses any $1$ row or $1$ column that contains an empty cell and fills all of its cells.
After person $N$, the turn returns to person $1$.
The person who fills the last cell loses.
Each person acts so as not to lose.
Output $YES$ if person $K$ loses, and $NO$ if they do not lose.

Input

$H\ W\ N\ K$

Line $1$ contains $H, W, N, K$ separated by spaces.
$1 \le H,W \le 10^9$
$1 \le N \le 10^{18}$
$1 \le K \le N$

Output

Output $YES$ if person $K$ loses, and $NO$ if they do not lose.

Sample

2 2 2 1

YES

1 2 2 1

NO

1 14 5 4

YES