F. Lost Array
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
My orzlers, we can optimize this problem from $O(S^3)$ to $O\left(T^\frac{5}{9}\right)$!
— Spyofgame, founder of Orzlim religion

A long time ago, Spyofgame invented the famous array $a$ ($1$-indexed) of length $n$ that contains information about the world and life. After that, he decided to convert it into the matrix $b$ ($0$-indexed) of size $(n + 1) \times (n + 1)$ which contains information about the world, life and beyond.

Spyofgame converted $a$ into $b$ with the following rules.

• $b_{i,0} = 0$ if $0 \leq i \leq n$;
• $b_{0,i} = a_{i}$ if $1 \leq i \leq n$;
• $b_{i,j} = b_{i,j-1} \oplus b_{i-1,j}$ if $1 \leq i, j \leq n$.

Here $\oplus$ denotes the bitwise XOR operation.

Today, archaeologists have discovered the famous matrix $b$. However, many elements of the matrix has been lost. They only know the values of $b_{i,n}$ for $1 \leq i \leq n$ (note that these are some elements of the last column, not the last row).

The archaeologists want to know what a possible array of $a$ is. Can you help them reconstruct any array that could be $a$?

Input

The first line contains a single integer $n$ ($1 \leq n \leq 5 \cdot 10^5$).

The second line contains $n$ integers $b_{1,n}, b_{2,n}, \ldots, b_{n,n}$ ($0 \leq b_{i,n} < 2^{30}$).

Output

If some array $a$ is consistent with the information, print a line containing $n$ integers $a_1, a_2, \ldots, a_n$. If there are multiple solutions, output any.

If such an array does not exist, output $-1$ instead.

Examples
Input
3
0 2 1

Output
1 2 3

Input
1
199633

Output
199633

Input
10
346484077 532933626 858787727 369947090 299437981 416813461 865836801 141384800 157794568 691345607

Output
725081944 922153789 481174947 427448285 516570428 509717938 855104873 280317429 281091129 1050390365

Note

If we let $a = [1,2,3]$, then $b$ will be:

 $\bf{0}$ $\bf{1}$ $\bf{2}$ $\bf{3}$ $\bf{0}$ $1$ $3$ $0$ $\bf{0}$ $1$ $2$ $2$ $\bf{0}$ $1$ $3$ $1$

The values of $b_{1,n}, b_{2,n}, \ldots, b_{n,n}$ generated are $[0,2,1]$ which is consistent with what the archaeologists have discovered.