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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)



import java.io.*;
import java.util.*;

public class Main {
    static StringBuilder sb = new StringBuilder();
    static FastScanner sc = new FastScanner(System.in);
    static int INF = 12345678;
    static long MOD = 1000000007;
    static int[] y4 = {0, 1, 0, -1};
    static int[] x4 = {1, 0, -1, 0};
    static int[] y8 = {0, 1, 0, -1, -1, 1, 1, -1};
    static int[] x8 = {1, 0, -1, 0, 1, -1, 1, -1};
    static long[] F;//factorial
    static boolean[] isPrime;
    static int[] primes;
    static char[][] map;

    static int N, M;
    static long T;
    static int[] A;


    public static void main(String[] args) {

        int n = sc.nextInt();

        long[] array = sc.nextLongArray(n);
        long[] ans = new long[n];

        StringBuilder sb = new StringBuilder();

        long mid;

        long l = 0;
        long r = 2000000020;

        boolean f = false;
        boolean skip = false;

        while(true){
            f = false;
            mid = (r + l) / 2;
            long temp = mid;

            for(int i = 0;i < n;i++){
                ans[i] = temp;
                temp = 2*array[i] - temp;

                if(temp < 0){
                    skip = true;
                    if(!f) {
                        r = mid;

                        break;
                    }else{
                        l = mid;
//                        System.out.println("l");
                        break;
                    }
                }
                f = !f;

            }
            if(!skip) {
                if (mid == temp) {

                    for (long i : ans) {
                        sb.append(i);
                        sb.append(" ");
                    }

                    System.out.println(sb.toString());

                    break;
                } else {
                    if (mid - temp > 0) {
                        r = mid;
                    } else {
                        l = mid;
                    }
                }
            }
            skip = false;

        }


    }

    static int max(int... a) {
        int res = Integer.MIN_VALUE;
        for (int i : a) {
            res = Math.max(res, i);
        }
        return res;
    }

    static long max(long... a) {
        long res = Long.MIN_VALUE;
        for (long i : a) {
            res = Math.max(res, i);
        }
        return res;
    }


    static int max(int[][] ar) {
        int res = Integer.MIN_VALUE;
        for (int i[] : ar)
            res = Math.max(res, max(i));
        return res;
    }

    static int min(int... a) {
        int res = Integer.MAX_VALUE;
        for (int i : a) {
            res = Math.min(res, i);
        }
        return res;
    }

    static long min(long... a) {
        long res = Long.MAX_VALUE;
        for (long i : a) {
            res = Math.min(res, i);
        }
        return res;
    }

    static int min(int[][] ar) {
        int res = Integer.MAX_VALUE;
        for (int i[] : ar)
            res = Math.min(res, min(i));
        return res;
    }

    static int sum(int[] a) {
        int cou = 0;
        for (int i : a)
            cou += i;
        return cou;
    }

    static int abs(int a) {
        return Math.abs(a);
    }


    static long abs(long a) {
        return Math.abs(a);
    }

    static class FastScanner {

        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        public String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        /*public String nextChar(){
            return (char)next()[0];
        }*/
        public String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }

            return tokenizer.nextToken("\n");
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        public int[] nextIntArrayDec(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt() - 1;
            }
            return a;
        }

        public int[][] nextIntArray2(int h, int w) {
            int[][] a = new int[h][w];
            for (int hi = 0; hi < h; hi++) {
                for (int wi = 0; wi < w; wi++) {
                    a[hi][wi] = nextInt();
                }
            }
            return a;
        }

        public int[][] nextIntArray2Dec(int h, int w) {
            int[][] a = new int[h][w];
            for (int hi = 0; hi < h; hi++) {
                for (int wi = 0; wi < w; wi++) {
                    a[hi][wi] = nextInt() - 1;
                }
            }
            return a;
        }

        //複数の配列を受け取る
        public void nextIntArrays2ar(int[] a, int[] b) {
            for (int i = 0; i < a.length; i++) {
                a[i] = sc.nextInt();
                b[i] = sc.nextInt();
            }
        }

        public void nextIntArrays2arDec(int[] a, int[] b) {
            for (int i = 0; i < a.length; i++) {
                a[i] = sc.nextInt() - 1;
                b[i] = sc.nextInt() - 1;
            }
        }

        //複数の配列を受け取る
        public void nextIntArrays3ar(int[] a, int[] b, int[] c) {
            for (int i = 0; i < a.length; i++) {
                a[i] = sc.nextInt();
                b[i] = sc.nextInt();
                c[i] = sc.nextInt();
            }
        }

        //複数の配列を受け取る
        public void nextIntArrays3arDecLeft2(int[] a, int[] b, int[] c) {
            for (int i = 0; i < a.length; i++) {
                a[i] = sc.nextInt() - 1;
                b[i] = sc.nextInt() - 1;
                c[i] = sc.nextInt();
            }
        }

        public Integer[] nextIntegerArray(int n) {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        public char[] nextCharArray(int n) {
            char[] a = next().toCharArray();

            return a;
        }

        public char[][] nextCharArray2(int h, int w) {
            char[][] a = new char[h][w];
            for (int i = 0; i < h; i++) {
                a[i] = next().toCharArray();
            }
            return a;
        }

        //スペースが入っている場合
        public char[][] nextCharArray2s(int h, int w) {
            char[][] a = new char[h][w];
            for (int i = 0; i < h; i++) {
                a[i] = nextLine().replace(" ", "").toCharArray();
            }
            return a;
        }

        public char[][] nextWrapCharArray2(int h, int w, char c) {
            char[][] a = new char[h + 2][w + 2];
            //char c = '*';
            int i;
            for (i = 0; i < w + 2; i++)
                a[0][i] = c;
            for (i = 1; i < h + 1; i++) {
                a[i] = (c + next() + c).toCharArray();
            }
            for (i = 0; i < w + 2; i++)
                a[h + 1][i] = c;
            return a;
        }

        //スペースが入ってる時用
        public char[][] nextWrapCharArray2s(int h, int w, char c) {
            char[][] a = new char[h + 2][w + 2];
            //char c = '*';
            int i;
            for (i = 0; i < w + 2; i++)
                a[0][i] = c;
            for (i = 1; i < h + 1; i++) {
                a[i] = (c + nextLine().replace(" ", "") + c).toCharArray();
            }
            for (i = 0; i < w + 2; i++)
                a[h + 1][i] = c;
            return a;
        }

        public long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextLong();
            }
            return a;
        }

        public long[][] nextLongArray2(int h, int w) {
            long[][] a = new long[h][w];
            for (int hi = 0; hi < h; hi++) {
                for (int wi = 0; wi < w; wi++) {
                    a[hi][wi] = nextLong();
                }
            }
            return a;
        }
    }
}