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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using System.Collections;

static class Extensions
{
    public static int ToInt(this string s) => int.Parse(s);
    public static long ToLong(this string s) => long.Parse(s);
    public static char ToChar(this string s) => char.Parse(s);
    public static double ToDouble(this string s) => double.Parse(s);
    public static int[] ToIntArray(this string s) => s.Replace(',', ' ').Split(' ').Select(x => x.ToInt()).ToArray();
    public static long[] ToLongArray(this string s) => s.Replace(',', ' ').Split(' ').Select(x => x.ToLong()).ToArray();
    public static double[] ToDoubleArray(this string s) => s.Replace(',', ' ').Split(' ').Select(x => x.ToDouble()).ToArray();
    public static Queue<T> ToQueue<T>(this IEnumerable<T> seq) => new Queue<T>(seq);
    public static Stack<T> ToStack<T>(this IEnumerable<T> seq) => new Stack<T>(seq);
    public static HashSet<T> ToHashSet<T>(this IEnumerable<T> seq) => new HashSet<T>(seq);
}
static class MyMath
{
    static public long GCD(long a, long b) => (a < b) ? GCD(b, a) : ((b == 0) ? a : GCD(b, a % b));
    static public long LCM(long a, long b) => (a > b) ? (a / GCD(a, b) * b) : (b / GCD(a, b) * a);
    static private readonly long _m = 1000000000 + 7;
    static public long Mod(long val) => (val % _m + _m) % _m;
    static private long ExtGCD(long a, long b, ref long x, ref long y) => (b == 0) ? (a + (x = 1) * 0 + (y = 0) * 0) : (ExtGCD(b, a % b, ref y, ref x) + (y -= a / b * x) * 0);
    static private long ModInverseInner(long a, long dummy1 = 0, long dummy2 = 0) => ExtGCD(a, _m, ref dummy1, ref dummy2) * 0 + Mod(dummy1);
    static public long ModInverse(long a) => ModInverseInner(a, 0, 0);
}

class Program
{
    static string[] ReadLines(int n) => Enumerable.Range(0, n).Select(s => Console.ReadLine()).ToArray();

    static void Main()
    {
        int N = Console.ReadLine().ToInt();
        var waterList = Console.ReadLine().ToLongArray();
        
        var ansList = new long[N];

        for (int i = 0; i < N; i++)
        {
            //山iに降った量を求める
            long val = 0;
            for (int j = i; j < i + N; j++)
            {
                val += ((j - i) % 2 == 0) ? waterList[j%N] : -waterList[j%N];
            }
            ansList[i] = val;
        }

        Console.WriteLine(string.Join(" ", ansList));
    }
    
}