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 namespace std;
int main() {
  int n, m, nq;
  scanf("%d %d %d", &n, &m, &nq);
  vector<int> perm(n), inv_perm(n);
  for (int i = 0; i < n; ++i) scanf("%d", &perm[i]), --perm[i];
  for (int i = 0; i < n; ++i) inv_perm[perm[i]] = i;
  vector<int> seq(m);
  for (int i = 0; i < m; ++i) {
    scanf("%d", &seq[i]), --seq[i];
    seq[i] = inv_perm[seq[i]];
  }
  vector<int> to_left(m), to_right(m);
  {
    vector<int> last(n, -1);
    for (int i = 0; i < m; ++i) {
      if (seq[i] == 0)
        to_left[i] = i;
      else {
        int prev = last[seq[i] - 1];
        if (prev == -1)
          to_left[i] = -1;
        else
          to_left[i] = to_left[prev];
      }
      last[seq[i]] = i;
    }
  }
  {
    vector<int> last(n, m);
    for (int i = m - 1; i >= 0; --i) {
      if (seq[i] == n - 1)
        to_right[i] = i;
      else {
        int next = last[seq[i] + 1];
        if (next == m)
          to_right[i] = m;
        else
          to_right[i] = to_right[next];
      }
      last[seq[i]] = i;
    }
  }
  vector<vector<int>> positions(n);
  for (int i = 0; i < m; ++i) positions[seq[i]].push_back(i);
  vector<int> smallest_end(m, m);
  for (int i = 0; i < m; ++i) {
    if (to_right[i] == m) continue;
    if (seq[i] == 0)
      smallest_end[i] = min(smallest_end[i], to_right[i]);
    else {
      vector<int> &prevs = positions[seq[i] - 1];
      if (prevs.empty()) continue;
      int l = 0, r = (int)prevs.size();
      while (l < r) {
        int mid = l + (r - l) / 2;
        int pos = prevs[mid];
        int from = to_left[pos];
        if (from > to_right[i])
          r = mid;
        else
          l = mid + 1;
      }
      if (l != (int)prevs.size()) {
        int pos = prevs[l];
        int from = to_left[pos];
        assert(from > to_right[i]);
        smallest_end[i] = min(smallest_end[i], pos);
      }
    }
  }
  struct query_t {
    int l, r;
    int id;
    bool result;
  };
  vector<query_t> queries(nq);
  for (int qid = 0; qid < nq; ++qid) {
    query_t &q = queries[qid];
    q.id = qid;
    scanf("%d %d", &q.l, &q.r), --q.l, --q.r;
  }
  sort(queries.begin(), queries.end(),
       [](const query_t &lhs, const query_t &rhs) { return lhs.l > rhs.l; });
  int cur_l = m - 1;
  int best_end = m;
  for (query_t &q : queries) {
    while (cur_l >= q.l) {
      best_end = min(best_end, smallest_end[cur_l]);
      --cur_l;
    }
    q.result = (q.r >= best_end);
  }
  sort(queries.begin(), queries.end(),
       [](const query_t &lhs, const query_t &rhs) { return lhs.id < rhs.id; });
  for (query_t &q : queries) printf("%d", (int)q.result);
  printf("\n");
  return 0;
}
