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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"math/rand"
	"time"
	"os"
	"bufio"
	"fmt"
	"strconv"
	"strings"
)

var(
	sc = bufio.NewScanner(os.Stdin)
)

func init()  {
	rand.Seed(time.Now().UnixNano())
	buf := make([]byte, 0) //ここのサイズは何でもよさそう
	sc.Buffer(buf, 1000000009)
}


//||||||||||||||||||||||||||入力|||||||||||||||||||||||||||||||||||||||\
//数字一文字入力
func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

//文字列を一行入力
func nextLine() string {
	sc.Scan()
	return sc.Text()
}

//空白区切りの文字列の入力
func spaceLine() []string {
	sc.Scan()
	return strings.Split(sc.Text()," ")
}

//数字を一行入力
func intLine() []int {
	str := spaceLine()
	buf := make([]int,len(str))
	for i,s:=range str{
		buf[i],_ = strconv.Atoi(s)
	}
	return buf
}

//|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

//ソートする
//sは最初のインデックス fは最後のインデックス
func Sort(ls []float64,l int,r int)  {
	if r - l <= 0{return}
	pipot := l + rand.Intn(r-l+1)
	ls[r],ls[pipot] = ls[pipot],ls[r]
	i := l
	for j:=l;j<r;j++{
		if ls[j] < ls[r]{
			ls[i],ls[j] = ls[j],ls[i]
			i ++
		}
	}
	ls[i],ls[r] = ls[r],ls[i]
	Sort(ls,l,i-1)
	Sort(ls,i+1,r)
}

//配列の大小を指定した要素で比較
//a < bならtrue
func sizeCheck(a []float64,b []float64,ls []int) bool {
	for i:= range ls{
		if a[i] < b[i]{
			return true
		} else if a[i] > b[i] {
			return false
		}
	}
	return false
}

//二次元配列のソート
func Sort2D(ls [][]float64,l int,r int,index []int)  {
	if r - l <= 0{return}
	pipot := l + rand.Intn(r-l+1)
	ls[r],ls[pipot] = ls[pipot],ls[r]
	i := l
	for j:=l;j<r;j++{
		if sizeCheck(ls[j],ls[r],index){
			ls[i],ls[j] = ls[j],ls[i]
			i ++
		}
	}
	ls[i],ls[r] = ls[r],ls[i]
	Sort2D(ls,l,i-1,index)
	Sort2D(ls,i+1,r,index)
}

func main() {
	n := nextInt()
	a := intLine()
	x := 0
	for i:=0;i<n;i++{
		if i % 2 == 0{
			x += a[i]
		} else {
			x -= a[i]
		}
	}
	x /= 2
	fmt.Print(x*2," ")
	for i:=0;i<n-1;i++{
		x = a[i] - x
		if i == n-2{
			fmt.Println(x*2)
			break
		}
		fmt.Print(x*2," ")
	}
}