A New Sequence

You are given a sequence $A = \{a_0, a_1, \dots, a_{N-1}\}$ of length $N$.

From it, define a new sequence $B = \{b_0, b_1, \dots, b_{N-1}\}$ of the same length:

$b_i = \sum_{k=0}^{N-1} (-1)^k (k+1) \, a_{(i+k) \bmod N}$

Indices are taken modulo $N$, so $a_{N}$ is $a_0$ and $a_{N+1}$ is $a_1$. In other words, $b_i$ starts at $a_i$, walks once around the sequence, and adds each $k$-th element multiplied by $(-1)^k (k+1)$.

Given the sequence $A$, compute the sequence $B$.

The first line contains $N$. ($1 \le N \le 300\,000$)

The second line contains $N$ integers $a_0, a_1, \dots, a_{N-1}$ separated by spaces. ($|a_i| \le 10^9$)

Print the $N$ integers $b_0, b_1, \dots, b_{N-1}$ of the sequence $B$ on one line, separated by spaces.

Only inputs for which $|b_i| \le 10^{18}$ holds for every $i$ are given.