#include <bits/stdc++.h>
using namespace std;
long long powerr(long long x, long long y);
long long mpower(long long x, long long y, long long p);
long long gcdExtended(long long a, long long b);
bool isPrime(long long n);
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t, j, k, l, h, p, q, r, x, i, y, z, a, b, c, d, n, m,
      M = 1000000007;
  char ch, ch2, ch3;
  string s1, s2, s3;
  set<pair<long long, long long> > S1, S;
  t = 1;
  x = 0;
  while (t--) {
    cin >> n >> q;
    long long A[n];
    for (i = 0; i < n; i++) cin >> A[i];
    if (q == 0) continue;
    z = 0;
    long long pos;
    for (i = 0; i < n; i++) {
      if (A[i] > z) {
        z = A[i];
        pos = i;
      }
    }
    vector<long long> v;
    for (i = pos + 1; i < n; i++) v.push_back(A[i]);
    long long num = A[0];
    vector<pair<long long, long long> > p;
    for (i = 1; i < pos + 1; i++) {
      p.push_back({num, A[i]});
      if (A[i] > num) {
        num = A[i];
      }
    }
    for (i = 0; i < pos; i++) {
      if (A[i] > A[i + 1]) {
        v.push_back(A[i + 1]);
        swap(A[i], A[i + 1]);
      } else
        v.push_back(A[i]);
    }
    for (i = 0; i < q; i++) {
      long long x;
      cin >> x;
      if (x <= pos) {
        cout << p[x - 1].first << " " << p[x - 1].second;
        cout << "\n";
      } else {
        y = (x - pos) % (n - 1);
        if (y == 0)
          y = n - 2;
        else
          y--;
        cout << z << " " << v[y];
        cout << "\n";
      }
    }
  }
}
long long gcdExtended(long long a, long long b) {
  if (b == 0) {
    return a;
  } else
    return gcdExtended(b, a % b);
}
long long mpower(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long powerr(long long x, long long y) {
  long long res = 1;
  while (y > 0) {
    if (y & 1) res = res * x;
    y = y >> 1;
    x = x * x;
  }
  return res;
}
bool isPrime(long long n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  long long p = sqrt(n);
  for (int i = 5; i <= p; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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;
long long powerr(long long x, long long y);
long long mpower(long long x, long long y, long long p);
long long gcdExtended(long long a, long long b);
bool isPrime(long long n);
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t, j, k, l, h, p, q, r, x, i, y, z, a, b, c, d, n, m,
      M = 1000000007;
  char ch, ch2, ch3;
  string s1, s2, s3;
  set<pair<long long, long long> > S1, S;
  t = 1;
  x = 0;
  while (t--) {
    cin >> n >> q;
    long long A[n];
    for (i = 0; i < n; i++) cin >> A[i];
    if (q == 0) continue;
    z = 0;
    long long pos;
    for (i = 0; i < n; i++) {
      if (A[i] > z) {
        z = A[i];
        pos = i;
      }
    }
    vector<long long> v;
    for (i = pos + 1; i < n; i++) v.push_back(A[i]);
    long long num = A[0];
    vector<pair<long long, long long> > p;
    for (i = 1; i < pos + 1; i++) {
      p.push_back({num, A[i]});
      if (A[i] > num) {
        num = A[i];
      }
    }
    for (i = 0; i < pos; i++) {
      if (A[i] > A[i + 1]) {
        v.push_back(A[i + 1]);
        swap(A[i], A[i + 1]);
      } else
        v.push_back(A[i]);
    }
    for (i = 0; i < q; i++) {
      long long x;
      cin >> x;
      if (x <= pos) {
        cout << p[x - 1].first << " " << p[x - 1].second;
        cout << "\n";
      } else {
        y = (x - pos) % (n - 1);
        if (y == 0)
          y = n - 2;
        else
          y--;
        cout << z << " " << v[y];
        cout << "\n";
      }
    }
  }
}
long long gcdExtended(long long a, long long b) {
  if (b == 0) {
    return a;
  } else
    return gcdExtended(b, a % b);
}
long long mpower(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long powerr(long long x, long long y) {
  long long res = 1;
  while (y > 0) {
    if (y & 1) res = res * x;
    y = y >> 1;
    x = x * x;
  }
  return res;
}
bool isPrime(long long n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  long long p = sqrt(n);
  for (int i = 5; i <= p; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}

```