#include <bits/stdc++.h>
using namespace std;
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
const int fx[4][2] = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
const int fxx[8][2] = {{0, 1}, {0, -1}, {1, 0},  {-1, 0},
                       {1, 1}, {1, -1}, {-1, 1}, {-1, -1}};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long n, q;
  cin >> n >> q;
  deque<long long> d;
  vector<long long> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    d.push_back(a[i]);
  }
  long long mx_pos = max_element((a).begin(), (a).end()) - a.begin();
  long long mx = *max_element((a).begin(), (a).end());
  vector<long long> query(q);
  set<long long> st;
  for (int i = 0; i < q; i++) {
    cin >> query[i];
    st.insert(query[i]);
  }
  map<long long, pair<int, int> > maap;
  long long f, s;
  for (int i = 1; i < 1e5 + 1; i++) {
    f = d.front();
    if (f == mx) {
      break;
    }
    d.pop_front();
    s = d.front();
    d.pop_front();
    if (st.count(i)) {
      maap[i] = make_pair(f, s);
    }
    if (f > s) {
      d.push_front(f);
      d.push_back(s);
    } else {
      d.push_front(s);
      d.push_back(f);
    }
  }
  for (int i = 0; i < n; i++) {
    f = d.front();
    d.pop_front();
    a[i] = f;
  };
  int qs = query.size();
  for (int i = 0; i < qs; i++) {
    if (maap.count(query[i])) {
      cout << maap[query[i]].first << " " << maap[query[i]].second << endl;
    } else {
      cout << mx << " " << a[(query[i] - mx_pos - 1) % (n - 1) + 1] << endl;
    }
  }
  return 0;
}

### Prompt

In CPP, your task is to solve the following problem:

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;
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
const int fx[4][2] = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
const int fxx[8][2] = {{0, 1}, {0, -1}, {1, 0},  {-1, 0},
                       {1, 1}, {1, -1}, {-1, 1}, {-1, -1}};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long n, q;
  cin >> n >> q;
  deque<long long> d;
  vector<long long> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    d.push_back(a[i]);
  }
  long long mx_pos = max_element((a).begin(), (a).end()) - a.begin();
  long long mx = *max_element((a).begin(), (a).end());
  vector<long long> query(q);
  set<long long> st;
  for (int i = 0; i < q; i++) {
    cin >> query[i];
    st.insert(query[i]);
  }
  map<long long, pair<int, int> > maap;
  long long f, s;
  for (int i = 1; i < 1e5 + 1; i++) {
    f = d.front();
    if (f == mx) {
      break;
    }
    d.pop_front();
    s = d.front();
    d.pop_front();
    if (st.count(i)) {
      maap[i] = make_pair(f, s);
    }
    if (f > s) {
      d.push_front(f);
      d.push_back(s);
    } else {
      d.push_front(s);
      d.push_back(f);
    }
  }
  for (int i = 0; i < n; i++) {
    f = d.front();
    d.pop_front();
    a[i] = f;
  };
  int qs = query.size();
  for (int i = 0; i < qs; i++) {
    if (maap.count(query[i])) {
      cout << maap[query[i]].first << " " << maap[query[i]].second << endl;
    } else {
      cout << mx << " " << a[(query[i] - mx_pos - 1) % (n - 1) + 1] << endl;
    }
  }
  return 0;
}

```