#include <bits/stdc++.h>
using namespace std;
const int iinf = 0x7fffffff;
const long long linf = ~(1LL << 63);
template <typename T>
inline T gcd(T a, T b) {
  if (a < 0) return gcd(-a, b);
  if (b < 0) return gcd(a, -b);
  if (a < b) return gcd(b, a);
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long qpow(long long a, long long n, long long mod) {
  a %= mod;
  long long ans = 1LL;
  while (n) {
    if (n & 1) ans = (ans * a % mod);
    a = (a * a % mod);
    n >>= 1;
  }
  return ans;
}
inline long long rev(long long a, long long p) { return qpow(a, p - 2, p); }
inline int in() {
  int x;
  cin >> x;
  return x;
}
inline void tic() {}
inline void toc() {}
const int maxn = 202000;
int b[maxn], c[maxn];
long long d[maxn];
long long dt = 0;
int a[maxn];
int cnti1[64];
int getbit(long long a, long long bit) {
  if (a & (1ll << bit)) return 1;
  return 0;
}
int n;
bool check() {
  memset(cnti1, 0, sizeof cnti1);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < 64; j++) {
      cnti1[j] += getbit(a[i], j);
    }
  }
  for (int i = 0; i < n; i++) {
    unsigned long long resB = 0, resC = 0;
    for (int j = 0; j < 33; j++) {
      if (getbit(a[i], j) == 1) {
        resB += (1uLL << j) * cnti1[j];
        resC += (1uLL << j) * n;
      } else {
        resC += (1uLL << j) * cnti1[j];
      }
    }
    if (resB != b[i] || resC != c[i]) return false;
  }
  return true;
}
int main() {
  ios::sync_with_stdio(0);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> b[i];
  for (int i = 0; i < n; i++) cin >> c[i];
  for (int i = 0; i < n; i++) {
    d[i] = b[i] + c[i];
    dt += d[i];
  }
  if (dt % (2 * n) != 0) {
    cout << -1 << endl;
    return 0;
  }
  dt = dt / 2 / n;
  for (int i = 0; i < n; i++) {
    if ((d[i] - dt) % n != 0) {
      cout << -1 << endl;
      return 0;
    }
    a[i] = (d[i] - dt) / n;
    if (a[i] < 0) {
      cout << -1 << endl;
      return 0;
    }
  }
  bool ok = check();
  if (ok) {
    for (int i = 0; i < n; i++) cout << a[i] << " ";
    cout << endl;
  } else {
    cout << -1 << endl;
  }
  return 0;
}

### Prompt

Generate a Cpp solution to 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 iinf = 0x7fffffff;
const long long linf = ~(1LL << 63);
template <typename T>
inline T gcd(T a, T b) {
  if (a < 0) return gcd(-a, b);
  if (b < 0) return gcd(a, -b);
  if (a < b) return gcd(b, a);
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long qpow(long long a, long long n, long long mod) {
  a %= mod;
  long long ans = 1LL;
  while (n) {
    if (n & 1) ans = (ans * a % mod);
    a = (a * a % mod);
    n >>= 1;
  }
  return ans;
}
inline long long rev(long long a, long long p) { return qpow(a, p - 2, p); }
inline int in() {
  int x;
  cin >> x;
  return x;
}
inline void tic() {}
inline void toc() {}
const int maxn = 202000;
int b[maxn], c[maxn];
long long d[maxn];
long long dt = 0;
int a[maxn];
int cnti1[64];
int getbit(long long a, long long bit) {
  if (a & (1ll << bit)) return 1;
  return 0;
}
int n;
bool check() {
  memset(cnti1, 0, sizeof cnti1);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < 64; j++) {
      cnti1[j] += getbit(a[i], j);
    }
  }
  for (int i = 0; i < n; i++) {
    unsigned long long resB = 0, resC = 0;
    for (int j = 0; j < 33; j++) {
      if (getbit(a[i], j) == 1) {
        resB += (1uLL << j) * cnti1[j];
        resC += (1uLL << j) * n;
      } else {
        resC += (1uLL << j) * cnti1[j];
      }
    }
    if (resB != b[i] || resC != c[i]) return false;
  }
  return true;
}
int main() {
  ios::sync_with_stdio(0);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> b[i];
  for (int i = 0; i < n; i++) cin >> c[i];
  for (int i = 0; i < n; i++) {
    d[i] = b[i] + c[i];
    dt += d[i];
  }
  if (dt % (2 * n) != 0) {
    cout << -1 << endl;
    return 0;
  }
  dt = dt / 2 / n;
  for (int i = 0; i < n; i++) {
    if ((d[i] - dt) % n != 0) {
      cout << -1 << endl;
      return 0;
    }
    a[i] = (d[i] - dt) / n;
    if (a[i] < 0) {
      cout << -1 << endl;
      return 0;
    }
  }
  bool ok = check();
  if (ok) {
    for (int i = 0; i < n; i++) cout << a[i] << " ";
    cout << endl;
  } else {
    cout << -1 << endl;
  }
  return 0;
}

```