#include <bits/stdc++.h>
using namespace std;
using ull = uint64_t;
using ll = int64_t;
using PII = pair<int, int>;
using VI = vector<int>;
string to_string(string s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
int main() {
  ios::sync_with_stdio(false), cin.tie(0);
  ull n, q;
  cin >> n >> q;
  VI A(n);
  deque<int> Q;
  for (int _n = n, i = 0; i < _n; ++i) {
    cin >> A[i];
    Q.push_back(A[i]);
  }
  vector<PII> small;
  for (int _n = n, i = 0; i < _n; ++i) {
    int a = Q.front();
    Q.pop_front();
    int b = Q.front();
    Q.pop_front();
    small.push_back({a, b});
    if (a > b) {
      Q.push_front(a);
      Q.push_back(b);
    } else {
      Q.push_front(b);
      Q.push_back(a);
    }
  }
  VI B(n);
  for (int _n = n, i = 0; i < _n; ++i) {
    int a = Q.front();
    Q.pop_front();
    B[i] = a;
  }
  while (q--) {
    ull k;
    cin >> k;
    if (k <= n) {
      cout << small[k - 1].first << " " << small[k - 1].second << '\n';
    } else {
      int idx = (k - n - 1) % (n - 1) + 1;
      cout << B[0] << " " << B[idx] << '\n';
    }
  }
}

### Prompt

Construct a CPP code solution to the problem outlined:

Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation.

For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2].

The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation.

Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque.

Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.

Input

The first line contains two integers n and q (2 ≤ n ≤ 10^5, 0 ≤ q ≤ 3 ⋅ 10^5) — the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≤ a_i ≤ 10^9) — the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≤ m_j ≤ 10^{18}).

Output

For each teacher's query, output two numbers A and B — the numbers that Valeriy pulls out of the deque for the m_j-th operation.

Examples

Input


5 3
1 2 3 4 5
1
2
10


Output


1 2
2 3
5 2


Input


2 0
0 0


Output

Note

Consider all 10 steps for the first test in detail:
  1. [1, 2, 3, 4, 5] — on the first operation, A and B are 1 and 2, respectively.

So, 2 we write to the beginning of the deque, and 1 — to the end.

We get the following status of the deque: [2, 3, 4, 5, 1].

  2. [2, 3, 4, 5, 1] ⇒ A = 2, B = 3.
  3. [3, 4, 5, 1, 2]
  4. [4, 5, 1, 2, 3]
  5. [5, 1, 2, 3, 4]
  6. [5, 2, 3, 4, 1]
  7. [5, 3, 4, 1, 2]
  8. [5, 4, 1, 2, 3]
  9. [5, 1, 2, 3, 4]
  10. [5, 2, 3, 4, 1] ⇒ A = 5, B = 2. 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ull = uint64_t;
using ll = int64_t;
using PII = pair<int, int>;
using VI = vector<int>;
string to_string(string s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
int main() {
  ios::sync_with_stdio(false), cin.tie(0);
  ull n, q;
  cin >> n >> q;
  VI A(n);
  deque<int> Q;
  for (int _n = n, i = 0; i < _n; ++i) {
    cin >> A[i];
    Q.push_back(A[i]);
  }
  vector<PII> small;
  for (int _n = n, i = 0; i < _n; ++i) {
    int a = Q.front();
    Q.pop_front();
    int b = Q.front();
    Q.pop_front();
    small.push_back({a, b});
    if (a > b) {
      Q.push_front(a);
      Q.push_back(b);
    } else {
      Q.push_front(b);
      Q.push_back(a);
    }
  }
  VI B(n);
  for (int _n = n, i = 0; i < _n; ++i) {
    int a = Q.front();
    Q.pop_front();
    B[i] = a;
  }
  while (q--) {
    ull k;
    cin >> k;
    if (k <= n) {
      cout << small[k - 1].first << " " << small[k - 1].second << '\n';
    } else {
      int idx = (k - n - 1) % (n - 1) + 1;
      cout << B[0] << " " << B[idx] << '\n';
    }
  }
}

```