Photoshoot

Farmer John is arranging his $n$ cows numbered $1$ to $n$ for a photoshoot. Initially, he planned for the $i$-th cow from the left to be the cow numbered a_i, and wrote down the permutation a_1, a_2, \ldots, a_n on a piece of paper. Unfortunately, that paper was stolen by Farmer Nhoj.

However, there might still be a chance for Farmer John to recover the permutation he originally wrote down. Before the paper was stolen, Bessie recorded the sequence b_1, b_2, \ldots, b_{n-1}, where b_i = a_i + a_{i+1} holds for each $i$ (1 \le i < n).

Based on Bessie's information, help Farmer John restore the lexicographically minimum permutation $a$ that could have produced $b$. A permutation $x$ is lexicographically smaller than a permutation $y$ if, for some $j$, x_i = y_i for all i < j and x_j < y_j (in other words, the two permutations are identical up to a certain point, at which $x$ first becomes smaller than $y$).

It is guaranteed that at least one such permutation $a$ exists.