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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
class Program{

    const long MOD =1000000007;
   
    static void Main(string[] args){
        int n = ScanOneInt();
        long[] ar = ScanLongArray(n);
        long[] ans = new long[n];
        long total = 0;
        for (int i = 0; i < n; i++)
        {
            total += ar[i];
        }
        for (int i = 0; i < n; i++)
        {
            if (i % 2 == 1)
            {
                total -= 2*ar[i];
            }
        }
        ans[0] = total;
        for (int i = 1; i < n; i++)
        {
            ans[i] = ar[i - 1] * 2 - ans[i-1];
        }

        foreach (var item in ans)
        {
            Console.Write(item+" ");
        }
        
    }

   
    static int Nibutan(long[] array, long k)
        // 以上・未満などをちゃんと見ること！
    {
        int low = 0 ;
        int high = array.Length-1;
        int mid = high;

        while (low < high)
        {
            mid = (low + high) / 2;
            if(array[mid] >= k) // k以上の最小index.ココを変えるだけ
            {
                high = mid;
            }
            else
            {
                low = mid + 1;
            }
            mid = (low + high) / 2;
        }
        return mid;
    }

    static int ScanOneInt()
    {
        return int.Parse(Console.ReadLine());
    }

    static long ScanOneLong()
    {
        return long.Parse(Console.ReadLine());
    }

    static int[] ScanIntArray(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        int[] ar = new int[t];
        for (int i = 0; i < t; i++)
        {
            ar[i] = int.Parse(str[i]);
        }
        return ar;
    }

    static Tuple<int,int> ScanTuple()
    {
        int[] tmp = ScanIntArray(2);
        return new Tuple<int, int>(tmp[0], tmp[1]);
    }
    static long[] ScanLongArray(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        long[] ar = new long[t];
        for (int i = 0; i < t; i++)
        {
            ar[i] = long.Parse(str[i]);
        }
        return ar;
    }

    static string[] ScanStringArray()
    {
        return Console.ReadLine().Split(' ');
    }

    static double[] ScanDoubleArray(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        double[] ar = new double[t];
        for (int i = 0; i < t; i++)
        {
            ar[i] = double.Parse(str[i]);
        }
        return ar;
    }


    static int[,] CombModMake()
    {
        int[,] res = new int[2005, 2005];
        for (int i = 0; i < 2005; i++)
        {
            for (int j = 0; j < 2005; j++)
            {
                if (i == 0 || i < j)
                {
                    res[i, j] = 0;
                }
                else if (j == 0 || i == j)
                {
                    res[i, j] = 1;
                }
                else
                {
                    res[i, j] = (res[i - 1, j] + res[i - 1, j - 1]) % (int)MOD;
                }
            }
        }
        return res;
    }

    static int Gcd (int a, int b)
    {
        if(b == 0)
        {
            return a;
        }
        else
        {
            return Gcd(b, a % b);
        }
    }

    static long Gcd_l(long a, long b)
    {
        if (b == 0)
        {
            return a;
        }
        else
        {
            return Gcd_l(b, a % b);
        }
    }


}

/*
 * pairのソート
        List<Tuple<int, int>> pairList = new List<Tuple<int, int>>();
        for (int i = 0; i < n; i++)
        {
            Tuple<int, int> tmp = ScanTuple();
            pairList.Add(tmp);
        }
        IOrderedEnumerable<Tuple<int, int>> sortedList = pairList.OrderBy(a => a.Item1).ThenBy(a => a.Item2);
*/