Problem:
Score : 400 points

Problem Statement

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

Output

Print N integers representing the number of liters of rain Mountain 1, Mountain 2, ..., Mountain N received, in this order.

Sample Input 1

3
2 2 4

Sample 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.

Sample Input 2

5
3 8 7 5 5

Sample Output 2

2 4 12 2 8

Sample Input 3

3
1000000000 1000000000 0

Sample Output 3

0 2000000000 0

Solution in Scala (2.11.7) (judge verdict: Accepted)

import java.io._
import java.util.StringTokenizer
import scala.util.control.Breaks.{breakable,break}
import scala.collection.mutable.Map
import scala.collection.mutable.Queue

object Main extends App {
  val in = new InputReader(System.in)
  val pw = new PrintWriter(System.out)

  val N = in.next().toInt
  val A = new Array[Int](N+1)
  for (i <- 1 to N)
    A(i) = in.next().toInt




  //
  def check(num: Int): Int = {
    val memo = new Array[Int](N+1)
    memo(1) = num
    memo(N) = num
    for (i <- 2 to N) {
      val tmp = A(i-1) - memo(i-1)
      memo(i-1) += tmp
      memo(i) += tmp
    }

    val res = A(N) - memo(N)
    Math.abs(res)
  }

  // 下に凸のグラフの最小値
  def ternarySearchInt(small: Int, big: Int): Int = {
    if(big - small <= 2) {
      val mid = (big + small) / 2
      if(check(big) <= check(mid)) big
      else if(check(small) <= check(mid)) small
      else mid
    }
    else{
      val midl = (big + small) / 2
      val midr = midl + 1
      if (check(midl) >= check(midr))
        ternarySearchInt(midl, big)
      else
        ternarySearchInt(small, midr)
    }
  }


  val ans = ternarySearchInt(0, 1e9.toInt)

  val memo = new Array[Int](N+1)
  val com = new Array[Int](N+1)
  memo(1) = ans
  memo(N) = ans
  com(1) = ans
  for (i <- 2 to N) {
    val tmp = A(i-1) - memo(i-1)
    com(i) = tmp
    memo(i-1) += tmp
    memo(i) += tmp
  }

  val res = A(N) - memo(N)
  Math.abs(res)

  pw.print(com(1)*2)
  for(i <- 2 to N)
    pw.print(s" ${com(i)*2}")
  pw.println
  pw.flush()
}


class InputReader(stream: InputStream) {
  private val reader = new BufferedReader(new InputStreamReader(stream))
  private var tokenizer: StringTokenizer = new StringTokenizer(reader.readLine())
  def next(): String = {
    while (!tokenizer.hasMoreTokens()) {
      tokenizer = new StringTokenizer(reader.readLine())
    }
    tokenizer.nextToken()
  }
}