Recently Lynyrd and Skynyrd went to a shop where Lynyrd bought a permutation p of length n, and Skynyrd bought an array a of length m, consisting of integers from 1 to n. 

Lynyrd and Skynyrd became bored, so they asked you q queries, each of which has the following form: "does the subsegment of a from the l-th to the r-th positions, inclusive, have a subsequence that is a cyclic shift of p?" Please answer the queries.

A permutation of length n is a sequence of n integers such that each integer from 1 to n appears exactly once in it.

A cyclic shift of a permutation (p_1, p_2, …, p_n) is a permutation (p_i, p_{i + 1}, …, p_{n}, p_1, p_2, …, p_{i - 1}) for some i from 1 to n. For example, a permutation (2, 1, 3) has three distinct cyclic shifts: (2, 1, 3), (1, 3, 2), (3, 2, 1).

A subsequence of a subsegment of array a from the l-th to the r-th positions, inclusive, is a sequence a_{i_1}, a_{i_2}, …, a_{i_k} for some i_1, i_2, …, i_k such that l ≤ i_1 < i_2 < … < i_k ≤ r.

Input

The first line contains three integers n, m, q (1 ≤ n, m, q ≤ 2 ⋅ 10^5) — the length of the permutation p, the length of the array a and the number of queries.

The next line contains n integers from 1 to n, where the i-th of them is the i-th element of the permutation. Each integer from 1 to n appears exactly once.

The next line contains m integers from 1 to n, the i-th of them is the i-th element of the array a.

The next q lines describe queries. The i-th of these lines contains two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m), meaning that the i-th query is about the subsegment of the array from the l_i-th to the r_i-th positions, inclusive.

Output

Print a single string of length q, consisting of 0 and 1, the digit on the i-th positions should be 1, if the subsegment of array a from the l_i-th to the r_i-th positions, inclusive, contains a subsequence that is a cyclic shift of p, and 0 otherwise.

Examples

Input

3 6 3
2 1 3
1 2 3 1 2 3
1 5
2 6
3 5


Output

110


Input

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


Output

010

Note

In the first example the segment from the 1-st to the 5-th positions is 1, 2, 3, 1, 2. There is a subsequence 1, 3, 2 that is a cyclic shift of the permutation. The subsegment from the 2-nd to the 6-th positions also contains a subsequence 2, 1, 3 that is equal to the permutation. The subsegment from the 3-rd to the 5-th positions is 3, 1, 2, there is only one subsequence of length 3 (3, 1, 2), but it is not a cyclic shift of the permutation.

In the second example the possible cyclic shifts are 1, 2 and 2, 1. The subsegment from the 1-st to the 2-nd positions is 1, 1, its subsequences are not cyclic shifts of the permutation. The subsegment from the 2-nd to the 3-rd positions is 1, 2, it coincides with the permutation. The subsegment from the 3 to the 4 positions is 2, 2, its subsequences are not cyclic shifts of the permutation.
#include <bits/stdc++.h>
struct seg_tree {
  std::vector<int> _data;
  int _n;
  seg_tree(const std::vector<int>& A) {
    int n = 1;
    while (n < A.size()) n++;
    _data = std::vector<int>(2 * n - 1);
    _n = n;
    for (int i = n - 1, j = 0; i < 2 * n - 1; i++, j++) _data[i] = A[j];
    for (int i = n - 2; i >= 0; i--)
      _data[i] = std::max(_data[2 * i + 1], _data[2 * (i + 1)]);
  }
  int query(int x, int y) {
    x += _n - 1;
    y += _n - 1;
    return internal_query(x, y);
  }
  int internal_query(int x, int y) {
    if (x > y) return -1;
    if (x == y) return _data[x];
    int result = -1;
    if (x % 2 == 0) {
      result = std::max(result, _data[x]);
      x += 1;
    }
    if (y % 2 == 1) {
      result = std::max(result, _data[y]);
      y -= 2;
    } else {
      y -= 1;
    }
    return std::max(result, internal_query(x / 2, y / 2));
  }
};
int main() {
  std::ios::sync_with_stdio(false);
  using namespace std;
  int n, m, q, tmp;
  cin >> n >> m >> q;
  map<int, int> M;
  for (int i = 0; i < n; i++) {
    cin >> tmp;
    M[tmp] = i;
  }
  vector<int> A(m), C(n, -1), D(m);
  for (int i = 0; i < m; i++) {
    cin >> tmp;
    A[i] = M[tmp];
  }
  const int max_log_n = 20;
  vector<vector<int> > B(max_log_n, vector<int>(m));
  for (int i = 0; i < m; i++) {
    B[0][i] = C[(A[i] - 1 + n) % n];
    C[A[i]] = i;
  }
  for (int i = 1; (1 << i) < m; i++)
    for (int j = 0; j < m; j++) {
      if (B[i - 1][j] == -1)
        B[i][j] = -1;
      else if (B[i - 1][B[i - 1][j]] == -1)
        B[i][j] = -1;
      else
        B[i][j] = B[i - 1][B[i - 1][j]];
    }
  for (int i = 0; i < m; i++) {
    int a = n - 1, j = i;
    while (a > 0 && j != -1) {
      int x = 0;
      while (a >= (1 << (x + 1))) x++;
      a -= (1 << x);
      j = B[x][j];
    }
    D[i] = j;
  }
  seg_tree E(D);
  vector<bool> answers(q);
  for (int i = 0; i < q; i++) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    int res = E.query(a, b);
    if (res >= a)
      answers[i] = true;
    else
      answers[i] = false;
  }
  for (int i = 0; i < q; i++) cout << "01"[answers[i]];
  cout << "\n";
  return 0;
}
