Hydrate

AtCoder

IDabc207_b

Time2000ms

Memory256MB

Difficulty—

There is a container with $A$ cyan balls. Takahashi will do the following operation as many times as he likes (possibly zero times): * add $B$ cyan balls and $C$ red balls into the container. Takahashi's objective is to reach a situation where the number of cyan balls in the container is at most $D$ times the number of red balls in it. Determine whether the objective is achievable. If it is achievable, find the minimum number of operations needed to achieve it. ## Constraints * $1 \leq A,B,C,D \leq 10^5$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $A$ $B$ $C$ $D$ [samples]

Samples

Input #1

5 2 3 2

Output #1

2

Before the first operation, the container has $5$ cyan balls and $0$ red balls. Since $5$ is greater than $0$ multiplied by $D=2$, Takahashi's objective is not yet achieved.
Just after the first operation, the container has $7$ cyan balls and $3$ red balls. Since $7$ is greater than $3$ multiplied by $2$, the objective is still not achieved.
Just after the second operation, the container has $9$ cyan balls and $6$ red balls. Since $9$ is not greater than $6$ multiplied by $2$, the objective is achieved.
Thus, the answer is $2$.

Input #2

6 9 2 3

Output #2

\-1

No matter how many times Takahashi repeats the operation, his objective will never be achieved.

API Response (JSON)

{
  "problem": {
    "name": "Hydrate",
    "description": {
      "content": "There is a container with $A$ cyan balls. Takahashi will do the following operation as many times as he likes (possibly zero times): *   add $B$ cyan balls and $C$ red balls into the container. Taka",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc207_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a container with $A$ cyan balls. Takahashi will do the following operation as many times as he likes (possibly zero times):\n\n*   add $B$ cyan balls and $C$ red balls into the container.\n\nTaka...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments