Magic 2

AtCoder

IDm_solutions2020_b

Time2000ms

Memory256MB

Difficulty—

M-kun has the following three cards: * A red card with the integer $A$. * A green card with the integer $B$. * A blue card with the integer $C$. He is a genius magician who can do the following operation at most $K$ times: * Choose one of the three cards and multiply the written integer by $2$. His magic is successful if both of the following conditions are satisfied after the operations: * The integer on the green card is **strictly** greater than the integer on the red card. * The integer on the blue card is **strictly** greater than the integer on the green card. Determine whether the magic can be successful. ## Constraints * $1 \leq A, B, C \leq 7$ * $1 \leq K \leq 7$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $A$ $B$ $C$ $K$ [samples]

Samples

Input #1

7 2 5
3

Output #1

Yes

The magic will be successful if, for example, he does the following operations:

*   First, choose the blue card. The integers on the red, green, and blue cards are now $7$, $2$, and $10$, respectively.
*   Second, choose the green card. The integers on the red, green, and blue cards are now $7$, $4$, and $10$, respectively.
*   Third, choose the green card. The integers on the red, green, and blue cards are now $7$, $8$, and $10$, respectively.

Input #2

7 4 2
3

Output #2

No

He has no way to succeed in the magic with at most three operations.

API Response (JSON)

{
  "problem": {
    "name": "Magic 2",
    "description": {
      "content": "M-kun has the following three cards: *   A red card with the integer $A$. *   A green card with the integer $B$. *   A blue card with the integer $C$. He is a genius magician who can do the followin",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "m_solutions2020_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "M-kun has the following three cards:\n\n*   A red card with the integer $A$.\n*   A green card with the integer $B$.\n*   A blue card with the integer $C$.\n\nHe is a genius magician who can do the followin...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments