Score : $500$ points

问题描述

对于正整数 $X$ 和 $Y$，在二维平面上满足以下条件的矩形被称为 好矩形。

• 每条边都与 $x$ 轴或 $y$ 轴平行。
• 对于每个顶点，其 $x$ 坐标是介于 $0$ 和 $X$（包括两端点）之间的整数，而 $y$ 坐标是介于 $0$ 和 $Y$（包括两端点）之间的整数。

判断是否可以在不重叠的情况下放置以下三个好矩形：一个面积至少为 $A$ 的好矩形、另一个面积至少为 $B$ 的好矩形，以及另一个面积至少为 $C$ 的好矩形。

这里，当任意两个矩形的交集面积为 $0$ 时，我们认为这三个矩形是非重叠的。

以上为通义千问 qwen-max 翻译，仅供参考。

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.

Sample Input 1

3 3 2 2 3

Sample Output 1

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.

Sample Input 2

3 3 4 4 1

Sample Output 2

No

There is no possible placement under the conditions.

Sample Input 3

1000000000 1000000000 1000000000000000000 1000000000000000000 1000000000000000000

Sample Output 3

No

update @ 2024/3/10 09:49:42