Rain Flows into Dams

AtCoder

IDabc133_d

Time2000ms

Memory256MB

Difficulty—

There are $N$ mountains in a circle, called Mountain $1$, Mountain $2$, $...$, Mountain $N$ in clockwise order. $N$ is an _odd_ number. Between these mountains, there are $N$ dams, called Dam $1$, Dam $2$, $...$, Dam $N$. Dam $i$ ($1 \leq i \leq N$) is located between Mountain $i$ and $i+1$ (Mountain $N+1$ is Mountain $1$). When Mountain $i$ ($1 \leq i \leq N$) receives $2x$ liters of rain, Dam $i-1$ and Dam $i$ each accumulates $x$ liters of water (Dam $0$ is Dam $N$). One day, each of the mountains received a non-negative **even** number of liters of rain. As a result, Dam $i$ ($1 \leq i \leq N$) accumulated a total of $A_i$ liters of water. Find the amount of rain each of the mountains received. We can prove that the solution is unique under the constraints of this problem. ## Constraints * All values in input are integers. * $3 \leq N \leq 10^5-1$ * $N$ is an odd number. * $0 \leq A_i \leq 10^9$ * The situation represented by input can occur when each of the mountains receives a non-negative even number of liters of rain. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

3
2 2 4

Output #1

4 0 4

If we assume Mountain $1$, $2$, and $3$ received $4$, $0$, and $4$ liters of rain, respectively, it is consistent with this input, as follows:

*   Dam $1$ should have accumulated $\frac{4}{2} + \frac{0}{2} = 2$ liters of water.
*   Dam $2$ should have accumulated $\frac{0}{2} + \frac{4}{2} = 2$ liters of water.
*   Dam $3$ should have accumulated $\frac{4}{2} + \frac{4}{2} = 4$ liters of water.

Input #2

5
3 8 7 5 5

Output #2

2 4 12 2 8

Input #3

3
1000000000 1000000000 0

Output #3

0 2000000000 0

API Response (JSON)

{
  "problem": {
    "name": "Rain Flows into Dams",
    "description": {
      "content": "There are $N$ mountains in a circle, called Mountain $1$, Mountain $2$, $...$, Mountain $N$ in clockwise order. $N$ is an _odd_ number. Between these mountains, there are $N$ dams, called Dam $1$, Dam",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc133_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ mountains in a circle, called Mountain $1$, Mountain $2$, $...$, Mountain $N$ in clockwise order. $N$ is an _odd_ number.\nBetween these mountains, there are $N$ dams, called Dam $1$, Dam...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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