Walking Takahashi

AtCoder

IDabc175_c

Time2000ms

Memory256MB

Difficulty—

Takahashi, who lives on the number line, is now at coordinate $X$. He will make exactly $K$ moves of distance $D$ in the positive or negative direction. More specifically, in one move, he can go from coordinate $x$ to $x + D$ or $x - D$. He wants to make $K$ moves so that the absolute value of the coordinate of the destination will be the smallest possible. Find the minimum possible absolute value of the coordinate of the destination. ## Constraints * $-10^{15} \leq X \leq 10^{15}$ * $1 \leq K \leq 10^{15}$ * $1 \leq D \leq 10^{15}$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $X$ $K$ $D$ [samples]

Samples

Input #1

6 2 4

Output #1

2

Takahashi is now at coordinate $6$. It is optimal to make the following moves:

*   Move from coordinate $6$ to ($6 - 4 =$) $2$.
*   Move from coordinate $2$ to ($2 - 4 =$) $-2$.

Here, the absolute value of the coordinate of the destination is $2$, and we cannot make it smaller.

Input #2

7 4 3

Output #2

1

Takahashi is now at coordinate $7$. It is optimal to make, for example, the following moves:

*   Move from coordinate $7$ to $4$.
*   Move from coordinate $4$ to $7$.
*   Move from coordinate $7$ to $4$.
*   Move from coordinate $4$ to $1$.

Here, the absolute value of the coordinate of the destination is $1$, and we cannot make it smaller.

Input #3

10 1 2

Output #3

Input #4

1000000000000000 1000000000000000 1000000000000000

Output #4

1000000000000000

The answer can be enormous.

API Response (JSON)

{
  "problem": {
    "name": "Walking Takahashi",
    "description": {
      "content": "Takahashi, who lives on the number line, is now at coordinate $X$. He will make exactly $K$ moves of distance $D$ in the positive or negative direction. More specifically, in one move, he can go from ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc175_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi, who lives on the number line, is now at coordinate $X$. He will make exactly $K$ moves of distance $D$ in the positive or negative direction.\nMore specifically, in one move, he can go from ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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