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:

<image>

where a and b means bitwise AND, while a or b 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 ≤ 200 000) — 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
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        AntonAndSchool solver = new AntonAndSchool();
        solver.solve(1, in, out);
        out.close();
    }

    static class AntonAndSchool {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int N = in.nextInt();
            long[] b = new long[N];
            long[] c = new long[N];
            long sum = 0;
            for (int i = 0; i < N; i++) {
                b[i] = in.nextInt();
                sum += b[i];
            }
            for (int i = 0; i < N; i++) {
                c[i] = in.nextInt();
                sum += c[i];
                if (c[i] < b[i]) {
                    out.println(-1);
                    return;
                }
            }
            if (sum % (2 * N) == 0) {
                sum /= 2 * N;
            } else {
                out.println(-1);
                return;
            }
            long[] a = new long[N];
            for (int i = 0; i < N; i++) {
                if ((b[i] + c[i] - sum) % N == 0) {
                    a[i] = (b[i] + c[i] - sum) / N;
                } else {
                    out.println(-1);
                    return;
                }
            }
            int[] count_active = new int[30];
            for (long el : a) {
                for (int i = 0; i < 30; i++) {
                    if ((el & (1 << i)) > 0) {
                        count_active[i]++;
                    }
                }
            }
            long[] b_test = new long[N];
            long[] c_test = new long[N];
            for (int i = 0; i < N; i++) {
                for (int j = 0; j < 30; j++) {
                    if ((a[i] & (1 << j)) > 0) {
                        c_test[i] += N * (1 << j);
                        b_test[i] += count_active[j] * (1 << j);
                    } else {
                        c_test[i] += count_active[j] * (1 << j);
                    }
                }
            }
            if (Arrays.equals(c, c_test) && Arrays.equals(b, b_test)) {
                for (long el : a) {
                    out.println(el);
                }
            } else {
                out.println(-1);
            }
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

