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>
constexpr int MAXN = 200005;
struct Data {
  int time;
  int last;
  bool may;
  int mayTime;
};
std::vector<Data> data[MAXN];
int n, m, q;
void add(int time, int val) {
  data[val].push_back(
      {time,
       (val == 0) ? time
                  : ((data[val - 1].empty()) ? -1 : data[val - 1].back().last),
       false});
  if (val == (n - 1)) {
    std::function<void(int val, int pos)> dfs = [&](int val, int pos) -> void {
      if (!data[val][pos].may) {
        data[val][pos].may = true;
        data[val][pos].mayTime = time;
        if (val) {
          auto it = std::upper_bound(
              data[val - 1].begin(), data[val - 1].end(), data[val][pos],
              [](const Data& first, const Data& second) -> bool {
                return first.time < second.time;
              });
          if (it != data[val - 1].begin()) {
            dfs(val - 1, (it - data[val - 1].begin()) - 1);
          }
        }
        if (pos) {
          dfs(val, pos - 1);
        }
      }
    };
    dfs(val, data[val].size() - 1);
  }
}
int info[MAXN];
int per[MAXN];
int help[MAXN];
int left[MAXN];
int main() {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(0);
  std::cout.tie(0);
  std::cin >> n >> m >> q;
  for (int i = 0; i < n; i++) {
    std::cin >> per[i];
    help[per[i] - 1] = i;
  }
  for (int i = 0; i < m; i++) {
    std::cin >> info[i];
    info[i] = help[info[i] - 1];
  }
  for (int i = 0; i < m; i++) {
    static int left = -1;
    add(i, info[i]);
    int pos = data[info[i]].back().last;
    if (pos != -1) {
      if (info[i] != (n - 1)) {
        int b = -1, e = data[info[i] + 1].size();
        while ((b + 1) < e) {
          int mm = (b + e) / 2;
          if ((data[info[i] + 1][mm].mayTime < pos) &&
              (data[info[i] + 1][mm].may)) {
            b = mm;
          } else {
            e = mm;
          }
        }
        if (b != -1) {
          left = std::max(left, data[info[i] + 1][b].time);
        }
      } else {
        left = std::max(left, pos);
      }
    }
    ::left[i] = left;
  }
  for (int i = 0; i < q; i++) {
    int l, r;
    std::cin >> l >> r;
    l--;
    r--;
    std::cout << "01"[left[r] >= l];
  }
  std::cout << '\n';
  return 0;
}
