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>
using u64 = unsigned long long;
template <class T>
std::vector<T> read(int n) {
  std::vector<T> res(n);
  for (auto& r : res) {
    std::cin >> r;
  }
  return res;
}
int lg_floor(u64 n) { return 63 - __builtin_clzll(n); }
int lg_ceil(u64 n) { return 63 - __builtin_clzll(2 * n - 1); }
template <class T>
struct RMQ {
  RMQ(const std::vector<T>& AA)
      : A(AA), M(lg_ceil(A.size() + 1), std::vector<int>(A.size())) {
    std::iota(begin(M[0]), end(M[0]), 0);
    for (size_t i = 0; i + 1 < M.size(); i++) {
      for (size_t j = 0; j + (1 << i) < M[i].size(); j++) {
        if (A[M[i][j]] < A[M[i][j + (1 << i)]]) {
          M[i + 1][j] = M[i][j];
        } else {
          M[i + 1][j] = M[i][j + (1 << i)];
        }
      }
    }
  }
  int operator()(int l, int r) {
    int k = lg_floor(r - l);
    if (A[M[k][l]] < A[M[k][r - (1 << k)]]) {
      return M[k][l];
    } else {
      return M[k][r - (1 << k)];
    }
  }
  std::vector<T> A;
  std::vector<std::vector<int>> M;
};
int main() {
  std::ios::sync_with_stdio(0), std::cin.tie(0), std::cout.tie(0);
  int n, m, q;
  std::cin >> n >> m >> q;
  auto p = read<int>(n);
  auto a = read<int>(m);
  for (int& v : p) v--;
  for (int& v : a) v--;
  std::vector<int> follow(n);
  for (int i = 0; i < n; i++) {
    follow[p[i]] = p[(i + 1) % n];
  }
  const int lg = lg_floor(n) + 1;
  std::vector<std::vector<int>> jump(lg, std::vector<int>(m + 1, m));
  std::vector<int> next(n, m);
  for (int i = m - 1; i >= 0; i--) {
    jump[0][i] = next[follow[a[i]]];
    next[a[i]] = i;
  }
  for (int j = 1; j < lg; j++) {
    for (int i = 0; i < m; i++) {
      jump[j][i] = jump[j - 1][jump[j - 1][i]];
    }
  }
  std::vector<int> end(m);
  for (int i = 0; i < m; i++) {
    end[i] = i;
    for (int j = 0; j < lg; j++) {
      if (((n - 1) >> j) & 1) {
        end[i] = jump[j][end[i]];
      }
    }
  }
  RMQ<int> rmq(end);
  while (q-- > 0) {
    int l, r;
    std::cin >> l >> r;
    l--;
    std::cout << (end[rmq(l, r)] < r);
  }
  std::cout << '\n';
}
