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;
vector<int> arrr, tree;
void build(int v, int l, int r) {
  if (l + 1 == r) {
    tree[v] = arrr[l];
  } else {
    int m = l + (r - l) / 2;
    build(2 * v + 1, l, m);
    build(2 * v + 2, m, r);
    tree[v] = min(tree[2 * v + 1], tree[2 * v + 2]);
  }
}
int query(int v, int l, int r, int ql, int qr) {
  if (qr <= l || ql >= r) {
    return 1e9;
  }
  if (ql <= l && r <= qr) {
    return tree[v];
  }
  int m = l + (r - l) / 2;
  return min(query(2 * v + 1, l, m, ql, qr), query(2 * v + 2, m, r, ql, qr));
}
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n, m, q;
  cin >> n >> m >> q;
  vector<int> perm(n);
  for (int i = 0; i < n; i++) {
    cin >> perm[i];
    perm[i]--;
  }
  vector<int> next(n), prev(n);
  for (int i = 0; i < n; i++) {
    next[perm[i]] = perm[(i + 1) % n];
    prev[next[perm[i]]] = perm[i];
  }
  vector<int> arr(m);
  for (int i = 0; i < m; i++) {
    cin >> arr[i];
    arr[i]--;
  }
  vector<vector<int>> nxt(20, vector<int>(m, 1e9));
  vector<vector<int>> cur_arr(n);
  for (int i = 0; i < m; i++) {
    int el = arr[i];
    cur_arr[el].push_back(i);
    for (int j : cur_arr[prev[el]]) {
      nxt[0][j] = i;
    }
    cur_arr[prev[el]].clear();
  }
  for (int i = 1; i < 20; i++) {
    for (int j = 0; j < m; j++) {
      if (nxt[i - 1][j] != 1e9) nxt[i][j] = nxt[i - 1][nxt[i - 1][j]];
    }
  }
  vector<int> nxtt(m);
  for (int i = 0; i < m; i++) {
    nxtt[i] = i;
    int curr = n - 1;
    int p = 0;
    while (curr > 0) {
      if (curr & 1) {
        if (nxtt[i] != 1e9) nxtt[i] = nxt[p][nxtt[i]];
      }
      p++;
      curr >>= 1;
    }
  }
  arrr = nxtt;
  tree.resize(4 * m);
  build(0, 0, m);
  for (int i = 0; i < q; i++) {
    int l, r;
    cin >> l >> r;
    l--;
    int ans = query(0, 0, m, l, r);
    if (ans < r) {
      cout << "1";
    } else {
      cout << "0";
    }
  }
  cout << endl;
  return 0;
}
