The Lifesaving Riddle

The Riddler kidnaps Gil Colson, the district attorney.

To escape, Colson must solve three riddles. Batman helps him with the first two, but the third one is too hard. Can you help him solve it?

The riddle works as follows:

1. The Riddler writes down and hides an integer array $a$ of length $n$.
2. He then cyclically shifts it left by some amount $x$, and subtracts the shifted array from the original element by element.
3. The resulting array $b$ (that is, the array with $b_i = a_i - a_{(i + x) \bmod n}$ for all $i$) is given to Colson.

Given array $b$, restore all possible shift values $x$ that could produce $b$ from some array $a$.

The first line contains a single integer $n$, the length of the original array ($1 \leqslant n \leqslant 10^6$).

The second line contains $n$ integers $b_1, b_2, \ldots, b_n$ separated by spaces, the elements of the array $b$ that the Riddler gave ($|b_i| \leqslant 10^9$).

Print $n - 1$ integers separated by spaces. The $i$-th of them is 1 if $x = i$ could have occurred, and 0 otherwise.

In the first example, the array $b$ could come from $a = [2, 4, 4]$ shifted left by 1, or from $a = [2, 2, 4]$ shifted left by 2.

In the first example, this array $b$ could not come from any $a$ shifted by 3, while shifts 1 or 4 work, for example with $a = [1, 2, 0, 3, 7, 3]$ and $a = [3, 7, 0, 3, 4, 5]$ respectively.

For the third example, one can show that such $b$ could not have been produced in the way described in the statement.