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;
using ll = long long int;
const int maxn = 18;
void ConstructJumpTo(vector<int>& pre, vector<int>& a,
                     vector<vector<int> >& jump_to) {
  int m = a.size();
  vector<int> latest(pre.size(), 0);
  for (int i = 1; i < m; i++) {
    int cur_val = a[i];
    int pre_val = pre[cur_val];
    jump_to[0][i] = latest[pre_val];
    latest[cur_val] = i;
  }
  for (int k = 1; k < maxn; k++) {
    for (int i = 1; i < m; i++) {
      int lower_order = jump_to[k - 1][i];
      jump_to[k][i] = jump_to[k - 1][lower_order];
    }
  }
}
void FindMaxLeft(int n, vector<vector<int> >& jump_to, vector<int>& max_left) {
  int m = max_left.size();
  for (int i = 1; i < m; i++) {
    int cur_pos = i;
    int base = 1;
    for (int k = 0; k < maxn; k++) {
      if ((n - 1) & base) {
        cur_pos = jump_to[k][cur_pos];
      }
      base <<= 1;
    }
    max_left[i] = cur_pos;
  }
  int latest_left = 0;
  for (int i = 1; i < m; i++) {
    latest_left = max(latest_left, max_left[i]);
    max_left[i] = latest_left;
  }
}
int main() {
  int n, m;
  vector<int> p;
  vector<int> a;
  cin >> n >> m;
  p.resize(n + 1);
  a.resize(m + 1);
  int q;
  cin >> q;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &p[i]);
  }
  for (int i = 1; i <= m; i++) {
    scanf("%d", &a[i]);
  }
  vector<int> pre(n + 1);
  p[0] = p[n];
  for (int i = 1; i <= n; i++) {
    pre[p[i]] = p[i - 1];
  }
  pre[0] = p[n];
  vector<vector<int> > jump_to(maxn, vector<int>(m + 1, 0));
  ConstructJumpTo(pre, a, jump_to);
  vector<int> max_left(m + 1, 0);
  FindMaxLeft(n, jump_to, max_left);
  while (q-- > 0) {
    int l, r;
    scanf("%d %d", &l, &r);
    if (max_left[r] >= l) {
      printf("1");
    } else {
      printf("0");
    }
  }
  puts("");
}
