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>
int n, m, q;
std::vector<int> perm, array, next[30], next_n_1th, perm_inv;
std::vector<std::vector<int>> array_inv;
std::vector<bool> checked;
char line[300005] = "";
int max2(int a, int b) { return a > b ? a : b; }
int min2(int a, int b) { return a < b ? a : b; }
class constseg {
 public:
  int left, right;
  int minnext;
  constseg *lc, *rc;
  constseg(int lbound, int rbound) {
    left = lbound, right = rbound;
    if (lbound < rbound) {
      int mid = (lbound + rbound) / 2;
      lc = new constseg(lbound, mid);
      rc = new constseg(mid + 1, rbound);
      minnext = min2(lc->minnext, rc->minnext);
    } else {
      lc = NULL, rc = NULL;
      if (next_n_1th[left] == -1)
        minnext = 987654321;
      else
        minnext = next_n_1th[left];
    }
  }
  int find(int lbound, int rbound) {
    if (lbound == left && rbound == right) return minnext;
    int mid = (left + right) / 2;
    if (lbound <= mid && rbound <= mid)
      return lc->find(lbound, rbound);
    else if (lbound <= mid && mid < rbound)
      return min2(lc->find(lbound, mid), rc->find(mid + 1, rbound));
    else if (mid < lbound)
      return rc->find(lbound, rbound);
    return -1;
  }
};
int main(void) {
  scanf("%d %d %d", &n, &m, &q);
  perm_inv = std::vector<int>(n + 1, -1);
  for (int i = 0; i < n; i++) {
    int temp = i + 1;
    scanf("%d", &temp);
    perm.push_back(temp);
    perm_inv[temp] = i;
  }
  array_inv = std::vector<std::vector<int>>(n + 1);
  for (int i = 0; i < m; i++) {
    int temp = i % n + 1;
    scanf("%d", &temp);
    array.push_back(temp);
    array_inv[temp].push_back(i);
  }
  for (int i = 0; i < 30; i++) next[i] = std::vector<int>(m, -1);
  next_n_1th = std::vector<int>(m, -1);
  std::vector<std::vector<int>> lastlinkedpositions(n + 1);
  for (int i = 0; i < m; i++) {
    int thisnum = array[i], prevnum = perm[(perm_inv[thisnum] + n - 1) % n];
    lastlinkedpositions[thisnum].push_back(i);
    for (int pos : lastlinkedpositions[prevnum]) {
      next[0][pos] = i;
    }
    lastlinkedpositions[prevnum].clear();
  }
  for (int i = 1; i < 30; i++)
    for (int pos = 0; pos < m; pos++) {
      if (next[i - 1][pos] == -1)
        next[i][pos] = -1;
      else
        next[i][pos] = next[i - 1][next[i - 1][pos]];
    }
  for (int pos = 0; pos < m; pos++) {
    next_n_1th[pos] = pos;
    for (int i = 0; i < 30 && next_n_1th[pos] != -1; i++)
      if ((n - 1) & (1 << i)) next_n_1th[pos] = next[i][next_n_1th[pos]];
  }
  constseg *root = new constseg(0, m - 1);
  for (int qq = 0; qq < q; qq++) {
    int l, r;
    scanf("%d %d", &l, &r);
    l--, r--;
    if (root->find(l, r) <= r)
      line[qq] = '1';
    else
      line[qq] = '0';
  }
  line[q] = 0;
  printf("%s", line);
  return 0;
}
