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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::*;

const SP: u8 = b' ';
const LF: u8 = b'\n';

struct CharacterInput<'a> {
    locked_stdin: StdinLock<'a>,
    bytes_buffer: Vec<u8>,
}

impl<'a> CharacterInput<'a> {
    fn read(&mut self, delimiter: u8) -> &[u8] {
        self.bytes_buffer.clear();

        let mut len = self
            .locked_stdin
            .read_until(delimiter, &mut self.bytes_buffer)
            .unwrap();

        if len > 0 {
            len -= 1;
        }

        &self.bytes_buffer[0..len]
    }

    fn scan_u(&mut self, delimiter: u8) -> u32 {
        self.read(delimiter)
            .into_iter()
            .fold(0, |accumulator, byte| {
                (byte - b'0') as u32 + accumulator * 10
            })
    }

    fn scan_u_vec(&mut self, n: usize, separator: u8, delimiter: u8) -> Vec<u32> {
        let mut vector = Vec::with_capacity(n as usize);
        for _i in 0..n - 1 {
            vector.push(self.scan_u(separator));
        }
        vector.push(self.scan_u(delimiter));
        vector
    }
}

fn create_cin<'a>(input: StdinLock<'a>, buffer_capacity: usize) -> CharacterInput {
    CharacterInput {
        locked_stdin: input,
        bytes_buffer: Vec::with_capacity(buffer_capacity),
    }
}

struct CharacterOutput {
    string_buffer: String,
}

impl CharacterOutput {
    fn push_s(&mut self, s: &str) {
        self.string_buffer += s;
    }

    fn push<T: ToString>(&mut self, n: T) {
        self.push_s(&n.to_string());
    }

    fn add<T: ToString>(&mut self, n: T, separator: char) {
        self.push(n);
        self.string_buffer.push(separator);
    }

    fn add_from_iterator<T: ToString, I>(
        &mut self,
        iterator: &mut I,
        length: usize,
        separator: char,
        delimiter: char,
    ) where
        I: Iterator<Item = T>,
    {
        for element in iterator.by_ref().take(length - 1) {
            self.add(element, separator);
        }
        self.add(iterator.next().unwrap(), delimiter);
    }

    fn flush(&mut self) {
        let out = stdout();
        let mut out = out.lock();
        out.write_all(self.string_buffer.as_bytes()).unwrap();
        self.string_buffer.clear();
    }
}

fn create_cout(capacity: usize) -> CharacterOutput {
    CharacterOutput {
        string_buffer: String::with_capacity(capacity),
    }
}

// ------------------------------------------------------------------------

trait StepSum: Iterator {
    fn step_sum(&mut self, step: usize) -> u32;
}

impl<I: Iterator> StepSum for I where I: Iterator<Item = u32> {
    fn step_sum(&mut self, step: usize) -> u32 {
        let mut acc;

        match self.next() {
            Some(value) => acc = value,
            None => return 0
        }

        loop {
            match self.nth(step - 1) {
                Some(value) => acc += value,
                None => break
            }
        }

        acc
    }    
}

fn main() {
    let cin = stdin();
    let cin = &mut create_cin(cin.lock(), 32);

    let n = cin.scan_u(LF) as usize;
    let a = cin.scan_u_vec(n, SP, LF);

    let total_rainfall = a.iter().sum::<u32>();
    let first_x = total_rainfall - 2 * a.iter().skip(1).map(|&v| v).step_sum(2);
    let mut rest_x_iterator = a.iter().take(n - 1).scan(first_x, |x, a| {
        *x = 2 * a - *x;
        Some(*x)
    });

    let cout = &mut create_cout(11 * n);
    cout.add(first_x, ' ');
    cout.add_from_iterator(&mut rest_x_iterator, n - 1, ' ', '\n');
    cout.flush();
}