#include <bits/stdc++.h>
using namespace std;
const int nmax = 2e5;
const int logmax = 40;
int f[logmax + 1];
long long a[nmax + 1], b[nmax + 1], c[nmax + 1];
int main() {
  int n;
  fscanf(stdin, "%d", &n);
  long long suma = 0;
  for (int i = 1; i <= n; ++i) {
    fscanf(stdin, "%I64d", &b[i]);
    suma += b[i];
  }
  for (int i = 1; i <= n; ++i) {
    fscanf(stdin, "%I64d", &c[i]);
    suma += c[i];
  }
  suma /= (2 * n);
  for (int i = 1; i <= n; ++i) {
    a[i] = (b[i] + c[i] - suma) / n;
    for (int j = 0; (1 << j) <= a[i]; ++j) {
      if (a[i] & (1 << j)) {
        ++f[j];
      }
    }
  }
  bool ok = 1;
  for (int i = 1; i <= n; ++i) {
    for (int j = 0; (1 << j) <= a[i]; ++j) {
      if (a[i] & (1 << j)) {
        b[i] -= (1LL << j) * f[j];
      }
    }
    if (b[i] != 0) ok = 0;
  }
  if (ok == 1) {
    for (int i = 1; i <= n; ++i) {
      fprintf(stdout, "%I64d ", a[i]);
    }
  } else {
    fprintf(stdout, "-1");
  }
  fprintf(stdout, "\n");
  return 0;
}

### Prompt

Create a solution in CPP for the following problem:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int nmax = 2e5;
const int logmax = 40;
int f[logmax + 1];
long long a[nmax + 1], b[nmax + 1], c[nmax + 1];
int main() {
  int n;
  fscanf(stdin, "%d", &n);
  long long suma = 0;
  for (int i = 1; i <= n; ++i) {
    fscanf(stdin, "%I64d", &b[i]);
    suma += b[i];
  }
  for (int i = 1; i <= n; ++i) {
    fscanf(stdin, "%I64d", &c[i]);
    suma += c[i];
  }
  suma /= (2 * n);
  for (int i = 1; i <= n; ++i) {
    a[i] = (b[i] + c[i] - suma) / n;
    for (int j = 0; (1 << j) <= a[i]; ++j) {
      if (a[i] & (1 << j)) {
        ++f[j];
      }
    }
  }
  bool ok = 1;
  for (int i = 1; i <= n; ++i) {
    for (int j = 0; (1 << j) <= a[i]; ++j) {
      if (a[i] & (1 << j)) {
        b[i] -= (1LL << j) * f[j];
      }
    }
    if (b[i] != 0) ok = 0;
  }
  if (ok == 1) {
    for (int i = 1; i <= n; ++i) {
      fprintf(stdout, "%I64d ", a[i]);
    }
  } else {
    fprintf(stdout, "-1");
  }
  fprintf(stdout, "\n");
  return 0;
}

```