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;
const int sz = 2e5 + 1;
int n, m, q;
int p[sz];
int b[sz];
int a[sz];
int t[sz];
int anc[sz][20];
int f[sz];
struct SegTree {
  vector<int> tree;
  void resize(int n) { tree.resize(4 * n); }
  void build(int l, int r, int v) {
    if (l == r) {
      tree[v] = t[l];
      return;
    }
    int md = (l + r) >> 1;
    build(l, md, 2 * v);
    build(md + 1, r, 2 * v + 1);
    tree[v] = max(tree[2 * v], tree[2 * v + 1]);
  }
  int get_max(int ql, int qr, int l, int r, int v) {
    if (ql > qr) return -1;
    if (ql == l && qr == r) return tree[v];
    int md = (l + r) >> 1;
    return max(get_max(ql, min(qr, md), l, md, 2 * v),
               get_max(max(ql, md + 1), qr, md + 1, r, 2 * v + 1));
  }
};
void solve() {
  cin >> n >> m >> q;
  for (int i = 0; i < n; i++) {
    cin >> p[i];
    b[p[i]] = i;
  }
  for (int i = 0; i < m; i++) cin >> a[i];
  if (n == 1) {
    for (int i = 0; i < q; i++) cout << 1;
    return;
  }
  for (int i = 0; i < sz; i++) {
    f[i] = -1;
    t[i] = -1;
  }
  vector<int> stack;
  for (int i = 0; i < m; i++) {
    int ind_pred = (b[a[i]] - 1 + n) % n;
    int pred = p[ind_pred];
    if (f[pred] != -1)
      anc[i][0] = f[pred];
    else
      anc[i][0] = -1;
    f[a[i]] = i;
  }
  for (int i = 1; i < 20; i++)
    for (int j = 0; j < m; j++) {
      if (anc[j][i - 1] == -1 || anc[anc[j][i - 1]][i - 1] == -1)
        anc[j][i] = -1;
      else
        anc[j][i] = anc[anc[j][i - 1]][i - 1];
    }
  for (int i = m - 1; i >= 0; i--) {
    int g = n - 1;
    int cur = i;
    for (int j = 19; j >= 0; j--)
      if ((1 << j) <= g) {
        g -= (1 << j);
        cur = anc[cur][j];
        if (cur == -1) break;
      }
    t[i] = cur;
  }
  string res = "";
  SegTree tree;
  tree.resize(m);
  tree.build(0, m - 1, 1);
  for (int i = 0; i < q; i++) {
    int l, r;
    cin >> l >> r;
    l--;
    r--;
    int o = tree.get_max(l, r, 0, m - 1, 1);
    if (o >= l)
      res += '1';
    else
      res += '0';
  }
  cout << res;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int q = 1;
  for (; q > 0; q--) {
    solve();
    cout << '\n';
  }
}
