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.Linq;
using System.Numerics;
using System.Collections.Generic;
using System.IO;
using System.Text;

public class Solver
{
    public void Solve()
    {
        int n = ri, t = 1;
        long s = 0;
        int[] a = new int[n];
        for(int i = 0; i < n; i++) { a[i] = ri; s += t * a[i]; t *= -1; }
        string[] b = new string[n];
        b[0] = s.ToString();
        for(int i = 1; i < n; i++)
        {
            s = a[i - 1] * 2 - s;
            b[i] = s.ToString();
        }
        Write(string.Join(" ", b));
    }

    int ri { get { return sc.Integer(); } }
    long rl { get { return sc.Long(); } }
    double rd { get { return sc.Double(); } }
    string rs { get { return sc.Scan(); } }
    public StreamScanner sc = new StreamScanner(Console.OpenStandardInput());
    
    private const long mod = 1000000007;
    long Reverse(long n) { return Pow(n, mod - 2); }
    int Abs(int n) { return (n > 0) ? n : -n; }
    int Gcd(params int[] n) { int p = n[0]; for (int i = 1; i < n.Length; i++) { p = Gcd(p, n[i]); } return p; }
    int Gcd(int a, int b) { return (a == 0) ? b : Gcd(b % a, a); }
    int Lcm(params int[] n) { int p = n[0]; for (int i = 1; i < n.Length; i++) { p = Lcm(p, n[i]); } return p; }
    int Lcm(int a, int b) { return a * b / Gcd(a, b); }
    int Max(params int[] n) { int p = n[0]; for (int i = 1; i < n.Length; i++) { p = (p > n[i]) ? p : n[i]; } return p; }
    int Min(params int[] n) { int p = n[0]; for (int i = 1; i < n.Length; i++) { p = (p < n[i]) ? p : n[i]; } return p; }
    long Mul(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = (p * n[i]) % mod; } return p; }
    long Pow(long n, long p) { long t = n, q = 1; while (p > 0) { if (p % 2 == 1) { q = (q * t) % mod; } t = (t * t) % mod; p /= 2; } return q; }
    long PowUpper(long n, long b) { long p = 1; while (p <= n) { p *= b; } return p; }
    long Abs(long n) { return (n > 0) ? n : -n; }
    long Gcd(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = Gcd(p, n[i]); } return p; }
    long Gcd(long a, long b) { return (a == 0) ? b : Gcd(b % a, a); }
    long Lcm(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = Lcm(p, n[i]); } return p; }
    long Lcm(long a, long b) { return a * b / Gcd(a, b); }
    long Max(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = (p > n[i]) ? p : n[i]; } return p; }
    long Min(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = (p < n[i]) ? p : n[i]; } return p; }
    void Write<T>(T t) { Console.WriteLine(t.ToString()); }
    void YN(bool t) { Console.WriteLine(t ? "YES" : "NO"); }
    void Yn(bool t) { Console.WriteLine(t ? "Yes" : "No"); }
    void yn(bool t) { Console.WriteLine(t ? "yes" : "no"); }
}

static class Program
{
    static public void Main(string[] args)
    {
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        var solver = new Solver();
        solver.Solve();
        Console.Out.Flush();
    }
}

public class StreamScanner
{
    public StreamScanner(Stream stream) { str = stream; }
    private readonly Stream str;
    private readonly byte[] buf = new byte[1024];
    private int len, ptr;
    public bool isEof = false;
    public bool IsEndOfStream { get { return isEof; } }
    private byte read()
    {
        if (isEof) throw new EndOfStreamException();
        if (ptr >= len)
        {
            ptr = 0;
            if ((len = str.Read(buf, 0, 1024)) <= 0)
            {
                isEof = true;
                return 0;
            }
        }
        return buf[ptr++];
    }
    public char Char()
    {
        byte b = 0;
        do b = read();
        while (b < 33 || 126 < b);
        return (char)b;
    }
    public string Scan()
    {
        var sb = new StringBuilder();
        for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
            sb.Append(b);
        return sb.ToString();
    }
    public long Long()
    {
        long ret = 0; byte b = 0; var ng = false;
        do b = read();
        while (b != '-' && (b < '0' || '9' < b));
        if (b == '-') { ng = true; b = read(); }
        for (; true; b = read())
        {
            if (b < '0' || '9' < b)
                return ng ? -ret : ret;
            else ret = ret * 10 + b - '0';
        }
    }
    public int Integer() { return (int)Long(); }
    public double Double() { return double.Parse(Scan()); }
}