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 n, m, q;
std::vector<int> p, a, asdasd, parent, parent_n, vis;
std::vector<vector<int>> g;
void dfs(int v, std::vector<int>& parents) {
  if (vis[v]) return;
  vis[v] = true;
  parents.push_back(v);
  if ((int)parents.size() - n >= 0)
    parent_n[v] = parents[(int)parents.size() - n];
  for (int u : g[v]) {
    dfs(u, parents);
  }
  parents.pop_back();
}
std::vector<int> tree;
void build(int v, int left, int right) {
  if (left + 1 == right) {
    tree[v] = parent_n[left];
    return;
  }
  int mid = (left + right) / 2;
  build(v << 1, left, mid);
  build((v << 1) + 1, mid, right);
  tree[v] = std::max(tree[v << 1], tree[(v << 1) + 1]);
}
int get_max(int v, int tl, int tr, int left, int right) {
  if (left <= tl && tr <= right) {
    return tree[v];
  }
  if (tr <= left || tl >= right) return -1;
  if (tr - tl < 2) {
    return -1;
  }
  int mid = (tl + tr) / 2;
  return std::max(get_max(v << 1, tl, mid, left, right),
                  get_max((v << 1) + 1, mid, tr, left, right));
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n >> m >> q;
  p.resize(n);
  a.resize(m);
  vector<int> pos(n);
  for (int i = 0; i < n; i++) {
    cin >> p[i];
    --p[i];
    pos[p[i]] = i;
  }
  for (int i = 0; i < m; i++) {
    cin >> a[i];
    --a[i];
  }
  asdasd.resize(n, -1);
  g.resize(m);
  parent.resize(m, -1);
  parent_n.resize(m, -1);
  vis.resize(m);
  for (int i = 0; i < m; i++) {
    parent[i] = asdasd[(pos[a[i]] - 1 + n) % n];
    if (parent[i] != -1) g[parent[i]].push_back(i);
    asdasd[pos[a[i]]] = i;
  }
  for (int i = 0; i < m; i++) {
    std::vector<int> parents;
    dfs(i, parents);
  }
  tree.resize(4 * m);
  build(1, 0, m);
  vector<pair<int, int>> queries(q);
  for (int i = 0; i < q; i++) {
    cin >> queries[i].first >> queries[i].second;
    queries[i].first--;
    int max = get_max(1, 0, m, queries[i].first, queries[i].second);
    std::cout << "01"[max >= queries[i].first];
  }
}
