E - Placing Rectangles

Score : $500$ points

Problem Statement

For positive integers $X$ and $Y$, a rectangle in a two-dimensional plane that satisfies the conditions below is said to be good.

• Every edge is parallel to the $x$- or $y$-axis.
• For every vertex, its $x$-coordinate is an integer between $0$ and $X$ (inclusive), and $y$-coordinate is an integer between $0$ and $Y$ (inclusive).

Determine whether it is possible to place the following three good rectangles without overlapping: a good rectangle of an area at least $A$, another of an area at least $B$, and another of an area at least $C$.

Here, three rectangles are considered to be non-overlapping when the intersection of any two of them has an area of $0$.

Constraints

• $1 \leq X, Y \leq 10^9$
• $1 \leq A, B, C \leq 10^{18}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$X$ $Y$ $A$ $B$ $C$

Output

If it is possible to place three rectangles under the conditions specified in the Problem Statement, print Yes; otherwise, print No.

3 3 2 2 3

Yes

The figure below shows a possible placement, where the number in a rectangle represents its area.

We can see that $2 \geq A, 3 \geq B, 3 \geq C$, satisfying the conditions.

3 3 4 4 1

No

There is no possible placement under the conditions.

1000000000 1000000000 1000000000000000000 1000000000000000000 1000000000000000000

No