A sequence of non-negative integers a_1, a_2, ..., a_n is called growing if for all i from 1 to n - 1 all ones (of binary representation) in a_i are in the places of ones (of binary representation) in a_{i + 1} (in other words, a_i \:\&\: a_{i + 1} = a_i, where \& denotes [bitwise AND](http://tiny.cc/xpy9uz)). If n = 1 then the sequence is considered growing as well.

For example, the following four sequences are growing: 

  * [2, 3, 15, 175] — in binary it's [10_2, 11_2, 1111_2, 10101111_2]; 
  * [5] — in binary it's [101_2]; 
  * [1, 3, 7, 15] — in binary it's [1_2, 11_2, 111_2, 1111_2]; 
  * [0, 0, 0] — in binary it's [0_2, 0_2, 0_2]. 



The following three sequences are non-growing: 

  * [3, 4, 5] — in binary it's [11_2, 100_2, 101_2]; 
  * [5, 4, 3] — in binary it's [101_2, 100_2, 011_2]; 
  * [1, 2, 4, 8] — in binary it's [0001_2, 0010_2, 0100_2, 1000_2]. 



Consider two sequences of non-negative integers x_1, x_2, ..., x_n and y_1, y_2, ..., y_n. Let's call this pair of sequences co-growing if the sequence x_1 ⊕ y_1, x_2 ⊕ y_2, ..., x_n ⊕ y_n is growing where ⊕ denotes [bitwise XOR](http://tiny.cc/bry9uz).

You are given a sequence of integers x_1, x_2, ..., x_n. Find the lexicographically minimal sequence y_1, y_2, ..., y_n such that sequences x_i and y_i are co-growing.

The sequence a_1, a_2, ..., a_n is lexicographically smaller than the sequence b_1, b_2, ..., b_n if there exists 1 ≤ k ≤ n such that a_i = b_i for any 1 ≤ i < k but a_k < b_k.

Input

The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow.

The first line of each test case contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5) — length of the sequence x_i.

The second line contains n integers x_1, x_2, ..., x_n (0 ≤ x_i < 2^{30}) — elements of the sequence x_i.

It is guaranteed that the sum of n overall all test cases doesn't exceed 2 ⋅ 10^5.

Output

For each test case, print n integers y_1, y_2, ..., y_n (0 ≤ y_i < 2^{30}) — lexicographically minimal sequence such that such that it's co-growing with given sequence x_i.

Example

Input


5
4
1 3 7 15
4
1 2 4 8
5
1 2 3 4 5
4
11 13 15 1
1
0


Output


0 0 0 0 
0 1 3 7 
0 1 0 3 2 
0 2 0 14 
0 
#include <iostream>
#include <algorithm>
#include <vector>
#include <string>
#include <cstring>
#include <map>
#include <set>
#include <map>
#include <unordered_map>
#include <deque>
#include <queue>
#include <cmath>
#include <math.h>
#include <unordered_set>
#include <fstream>
#include <sstream>
#include <stdio.h>
#include <climits>
#include <utility>
#include <iterator>
#include <limits>
#include <tuple>
#include <iomanip>
#include <random>
#include <ctime>
#include <chrono>
#include <random>

#define ull unsigned long long int
#define ll long long int
#define ld long double
#define pb push_back
#define str std::string
#define vec std::vector
#define hash_table std::unordered_map
#define prnt(v, end) \
  for (auto i : v)   \
    std::cout << i << end;
#define print(arr, n, end)    \
  for (int i = 0; i < n; ++i) \
    std::cout << arr[i] << end;
#define endl std::cout << "\n";
#define FASTIO                      \
  std::ios::sync_with_stdio(false); \
  std::cin.tie(nullptr);            \
  std::cout.tie(nullptr);

const int inf = 1e9 + 7;
const int64_t INF = 1e18 + 7;
const double pi = 2 * acos(0);
int64_t gcd(int64_t a, int64_t b) { return b == 0 ? a : gcd(b, a % b); }
int64_t lcm(int64_t a, int64_t b) { return a / gcd(a, b) * b; }
int64_t len(int64_t n)
{
  int64_t i = 0;
  while (n > 0)
  {
    ++i;
    n /= 10;
  }
  return i;
}
ull mod_pow(ull a, ull b, ull m = INF)
{
  ull res = 1;
  while (b > 0)
  {
    if (b & 1)
    {
      res *= (ull)a % m;
      res %= m;
    }
    a *= (ull)a % m;
    a %= m;
    b >>= 1;
  }
  return res % m;
}
int64_t prime_mod_inv(int64_t a, int64_t p) { return mod_pow(a, p - 2, p); }
bool is_prime(int64_t x)
{
  if (x <= 3)
    return x >= 2;
  if (x % 2 == 0)
    return false;
  for (int64_t d = 3; d * d <= x; d += 2)
  {
    if (x % d == 0)
      return false;
  }
  return true;
}
int64_t modinv(int a, int m)
{
  int64_t m0 = m, y = 0, x = 1;
  if (m == 1)
    return 0;
  while (a > 1)
  {
    int64_t q = a / m, t = m;
    m = a % m;
    a = t;
    t = y;
    y = x - q * y;
    x = t;
  }
  if (x < 0)
    x += m0;
  return x;
}

bool allSet(int n)
{
  return (((n + 1) & n) == 0);
}
bool kthSet(int n, int k)
{
  return n & (1LL << k);
}

int main()
{
  FASTIO;
  int t;
  std::cin >> t;
  while (t--)
  {
    int n;
    std::cin >> n;
    vec<int> x(n);
    for (int i = 0; i < n; ++i)
      std::cin >> x[i];
    vec<int> y(n, 0);
    for (int i = 0; i + 1 < n; ++i)
    {
      int a = y[i] ^ x[i];
      for (int k = 31; k >= 0; --k)
        if (kthSet(a, k) && !kthSet(x[i + 1], k))
        {
          y[i + 1] += 1LL << k;
        }
    }
    for (int in : y)
      std::cout << in << " ";
    endl;
  }
}
