#include <bits/stdc++.h>
using namespace std;
using ll = long long;
string to_string(string s) { return '"' + s + '"'; }
string to_string(bool b) { return (b ? "true" : "false"); }
string to_string(char c) {
  string s(1, c);
  return "'" + s + "'";
}
template <class T>
string to_string(vector<T> v) {
  string s = "{";
  bool first = true;
  for (T x : v) {
    if (!first) s += ", ";
    s += to_string(x);
    first = false;
  }
  s += "}";
  return s;
}
template <class T>
string to_string(set<T> v) {
  string s = "{";
  bool first = true;
  for (T x : v) {
    if (!first) s += ", ";
    s += to_string(x);
    first = false;
  }
  s += "}";
  return s;
}
template <class T>
string to_string(unordered_set<T> v) {
  string s = "{";
  bool first = true;
  for (T x : v) {
    if (!first) s += ", ";
    s += to_string(x);
    first = false;
  }
  s += "}";
  return s;
}
template <class T>
string to_string(multiset<T> v) {
  string s = "{";
  bool first = true;
  for (T x : v) {
    if (!first) s += ", ";
    s += to_string(x);
    first = false;
  }
  s += "}";
  return s;
}
template <class T1, class T2>
string to_string(pair<T1, T2> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <class T1, class T2>
string to_string(unordered_map<T1, T2> m) {
  string s = "{";
  bool first = true;
  for (auto x : m) {
    if (!first) s += ", ";
    s += "(" + to_string(x.first) + " -> " + to_string(x.second) + ")";
    first = false;
  }
  s += "}";
  return s;
}
template <class T1, class T2>
string to_string(map<T1, T2> m) {
  string s = "{";
  bool first = true;
  for (auto x : m) {
    if (!first) s += ", ";
    s += "(" + to_string(x.first) + " -> " + to_string(x.second) + ")";
    first = false;
  }
  s += "}";
  return s;
}
int m, n;
bool can_joy(vector<vector<int>> p, ll joy) {
  bool flag1 = false;
  for (int i = 0; i < m; i++) {
    int found = 0;
    for (int j = 0; j < n; j++) {
      found += p[i][j] >= joy;
    }
    if (found >= 2) {
      flag1 = true;
      break;
    }
  }
  if (!flag1) return false;
  bool flag2;
  for (int j = 0; j < n; j++) {
    flag2 = false;
    for (int i = 0; i < m; i++) {
      flag2 |= p[i][j] >= joy;
    }
    if (!flag2) return false;
  }
  return true;
}
void solve() {
  cin >> m >> n;
  vector<vector<int>> p(m, vector<int>(n));
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < n; j++) {
      cin >> p[i][j];
    }
  }
  ll l = 1, r = 1e9, mid;
  while (l < r) {
    ;
    ;
    mid = l + (r - l + 1) / 2;
    bool b = can_joy(p, mid);
    if (b)
      l = mid;
    else
      r = mid - 1;
  }
  assert(l == r);
  cout << l << "\n";
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t;
  cin >> t;
  while (t--) solve();
}

### Prompt

Construct a cpp code solution to the problem outlined:

Vlad has n friends, for each of whom he wants to buy one gift for the New Year.

There are m shops in the city, in each of which he can buy a gift for any of his friends. If the j-th friend (1 ≤ j ≤ n) receives a gift bought in the shop with the number i (1 ≤ i ≤ m), then the friend receives p_{ij} units of joy. The rectangular table p_{ij} is given in the input.

Vlad has time to visit at most n-1 shops (where n is the number of friends). He chooses which shops he will visit and for which friends he will buy gifts in each of them.

Let the j-th friend receive a_j units of joy from Vlad's gift. Let's find the value α=min\\{a_1, a_2, ..., a_n\}. Vlad's goal is to buy gifts so that the value of α is as large as possible. In other words, Vlad wants to maximize the minimum of the joys of his friends.

For example, let m = 2, n = 2. Let the joy from the gifts that we can buy in the first shop: p_{11} = 1, p_{12}=2, in the second shop: p_{21} = 3, p_{22}=4.

Then it is enough for Vlad to go only to the second shop and buy a gift for the first friend, bringing joy 3, and for the second — bringing joy 4. In this case, the value α will be equal to min\{3, 4\} = 3

Help Vlad choose gifts for his friends so that the value of α is as high as possible. Please note that each friend must receive one gift. Vlad can visit at most n-1 shops (where n is the number of friends). In the shop, he can buy any number of gifts.

Input

The first line of the input contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input.

An empty line is written before each test case. Then there is a line containing integers m and n (2 ≤ n, 2 ≤ n ⋅ m ≤ 10^5) separated by a space — the number of shops and the number of friends, where n ⋅ m is the product of n and m.

Then m lines follow, each containing n numbers. The number in the i-th row of the j-th column p_{ij} (1 ≤ p_{ij} ≤ 10^9) is the joy of the product intended for friend number j in shop number i.

It is guaranteed that the sum of the values n ⋅ m over all test cases in the test does not exceed 10^5.

Output

Print t lines, each line must contain the answer to the corresponding test case — the maximum possible value of α, where α is the minimum of the joys from a gift for all of Vlad's friends.

Example

Input


5

2 2
1 2
3 4

4 3
1 3 1
3 1 1
1 2 2
1 1 3

2 3
5 3 4
2 5 1

4 2
7 9
8 1
9 6
10 8

2 4
6 5 2 1
7 9 7 2


Output


3
2
4
8
2

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
string to_string(string s) { return '"' + s + '"'; }
string to_string(bool b) { return (b ? "true" : "false"); }
string to_string(char c) {
  string s(1, c);
  return "'" + s + "'";
}
template <class T>
string to_string(vector<T> v) {
  string s = "{";
  bool first = true;
  for (T x : v) {
    if (!first) s += ", ";
    s += to_string(x);
    first = false;
  }
  s += "}";
  return s;
}
template <class T>
string to_string(set<T> v) {
  string s = "{";
  bool first = true;
  for (T x : v) {
    if (!first) s += ", ";
    s += to_string(x);
    first = false;
  }
  s += "}";
  return s;
}
template <class T>
string to_string(unordered_set<T> v) {
  string s = "{";
  bool first = true;
  for (T x : v) {
    if (!first) s += ", ";
    s += to_string(x);
    first = false;
  }
  s += "}";
  return s;
}
template <class T>
string to_string(multiset<T> v) {
  string s = "{";
  bool first = true;
  for (T x : v) {
    if (!first) s += ", ";
    s += to_string(x);
    first = false;
  }
  s += "}";
  return s;
}
template <class T1, class T2>
string to_string(pair<T1, T2> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <class T1, class T2>
string to_string(unordered_map<T1, T2> m) {
  string s = "{";
  bool first = true;
  for (auto x : m) {
    if (!first) s += ", ";
    s += "(" + to_string(x.first) + " -> " + to_string(x.second) + ")";
    first = false;
  }
  s += "}";
  return s;
}
template <class T1, class T2>
string to_string(map<T1, T2> m) {
  string s = "{";
  bool first = true;
  for (auto x : m) {
    if (!first) s += ", ";
    s += "(" + to_string(x.first) + " -> " + to_string(x.second) + ")";
    first = false;
  }
  s += "}";
  return s;
}
int m, n;
bool can_joy(vector<vector<int>> p, ll joy) {
  bool flag1 = false;
  for (int i = 0; i < m; i++) {
    int found = 0;
    for (int j = 0; j < n; j++) {
      found += p[i][j] >= joy;
    }
    if (found >= 2) {
      flag1 = true;
      break;
    }
  }
  if (!flag1) return false;
  bool flag2;
  for (int j = 0; j < n; j++) {
    flag2 = false;
    for (int i = 0; i < m; i++) {
      flag2 |= p[i][j] >= joy;
    }
    if (!flag2) return false;
  }
  return true;
}
void solve() {
  cin >> m >> n;
  vector<vector<int>> p(m, vector<int>(n));
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < n; j++) {
      cin >> p[i][j];
    }
  }
  ll l = 1, r = 1e9, mid;
  while (l < r) {
    ;
    ;
    mid = l + (r - l + 1) / 2;
    bool b = can_joy(p, mid);
    if (b)
      l = mid;
    else
      r = mid - 1;
  }
  assert(l == r);
  cout << l << "\n";
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t;
  cin >> t;
  while (t--) solve();
}

```