Placing Rectangles

AtCoder

IDabc223_e

Time2000ms

Memory256MB

Difficulty—

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: $X$ $Y$ $A$ $B$ $C$ [samples]

Samples

Input #1

3 3 2 2 3

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.
![image](https://img.atcoder.jp/ghi/abc223e_sample.png)

Input #2

3 3 4 4 1

Output #2

No

There is no possible placement under the conditions.

Input #3

1000000000 1000000000 1000000000000000000 1000000000000000000 1000000000000000000

Output #3

No

API Response (JSON)

{
  "problem": {
    "name": "Placing Rectangles",
    "description": {
      "content": "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 eve",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc223_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "For positive integers $X$ and $Y$, a rectangle in a two-dimensional plane that satisfies the conditions below is said to be **good**.\n\n*   Every edge is parallel to the $x$\\- or $y$\\-axis.\n*   For eve...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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