Problem1922--Anton and School

1922: Anton and School

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Anton goes to school, his favorite lessons are arraystudying. He usually solves all the tasks pretty fast, but this time the teacher gave him a complicated one: given two arrays b and c of length n, find array a, such that:

where aandb means bitwise AND, while aorb means bitwise OR.

Usually Anton is good in arraystudying, but this problem is too hard, so Anton asks you to help.

Input

The first line of the input contains a single integers n (1≤n≤200000)− the size of arrays b and c.

The second line contains n integers bi (0≤bi≤109)− elements of the array b.

Third line contains n integers ci (0≤ci≤109)− elements of the array c.

Output

If there is no solution, print -1.

Otherwise, the only line of the output should contain n non-negative integers ai− elements of the array a. If there are multiple possible solutions, you may print any of them.

Examples
Input
4
6 8 4 4
16 22 10 10
Output
3 5 1 1 
Input
5
8 25 14 7 16
19 6 9 4 25
Output
-1

Source/Category