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 int64_t INF = 1e18;
const int64_t LOG = 20;
int32_t main() {
  int64_t n, m, q;
  cin >> n >> m >> q;
  vector<int64_t> p(n), pos(n);
  for (int64_t i = 0; i < n; i++) cin >> p[i], p[i]--, pos[p[i]] = i;
  vector<int64_t> last(n, 0);
  vector<int64_t> a(m + 1);
  vector<vector<int64_t> > jump(m + 1, vector<int64_t>(LOG, 0));
  for (int64_t i = 1; i < m + 1; i++) {
    cin >> a[i], a[i]--;
    int64_t pp = (pos[a[i]] + n - 1) % n;
    jump[i][0] = last[pp];
    last[pos[a[i]]] = i;
  }
  for (int64_t j = 1; j < LOG; j++)
    for (int64_t i = 1; i < m + 1; i++)
      jump[i][j] = jump[jump[i][j - 1]][j - 1];
  vector<int64_t> left(m + 1, 0);
  for (int64_t i = 1; i < m + 1; i++) {
    int64_t cur = i;
    for (int64_t j = 0; j < LOG; j++)
      if ((n - 1) & (int64_t(1) << j)) cur = jump[cur][j];
    left[i] = cur;
  }
  for (int64_t i = 1; i < m + 1; i++) left[i] = max(left[i], left[i - 1]);
  for (int64_t i = 0; i < q; i++) {
    int64_t l, r;
    cin >> l >> r;
    cout << (left[r] >= l ? 1 : 0);
  }
  cout << endl;
  return 0;
}
