102234: [AtCoder]ABC223 E - Placing Rectangles
Description
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.
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
Input
题意翻译
### 题目大意 问能否通过摆放平面中三个面积分别**至少**为 $A,B,C$ 的小矩形使得它们能被一个 $X\times Y$ 的矩形完全包含。 ### 数据范围 + $1\le X,Y \le 10^9$； + $1 \le A,B,C \le 10^{18}$。 ### 样例 1 解释 下图是三个小矩形的一种摆放方法。  其中 $2 \ge A$，$3\ge B$，$3 \ge C$，所以这种摆放方式是满足条件的。Output
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，它的$x$坐标在0和$X$（含）之间，$y$坐标在0和$Y$（含）之间。
确定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，另一个面积至少为$C$的好矩形。
这里，当任何两个矩形的交集面积为0时，认为三个矩形是不重叠的。
约束条件
- $1 \leq X, Y \leq 10^9$
- $1 \leq A, B, C \leq 10^{18}$
- 输入中的所有值都是整数。
输入
输入将以以下格式从标准输入给出：
$X$ $Y$ $A$ $B$ $C$
输出
如果可以在问题描述中指定的条件下放置三个矩形，则打印Yes；否则，打印No。
样例输入1
3 3 2 2 3
样例输出1
Yes
下图显示了一种可能的放置方式，矩形中的数字表示其面积。
我们可以看到$2 \geq A, 3 \geq B, 3 \geq C$，满足条件。
样例输入2
3 3 4 4 1
样例输出2
No
在这些条件下没有可能的放置方式。
样例输入3
1000000000 1000000000 1000000000000000000 1000000000000000000 1000000000000000000
样例输出3
No