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 vi = vector<int>;
const int LOG = 17;
const int inf = 1e9;
template <typename T>
struct RMQ {
  vector<vector<T>> spr;
  RMQ(const vector<T>& v) : spr(1, v) {
    for (int j = 1; (1 << j) <= (int)v.size(); ++j) {
      spr.push_back(vector<T>((int)v.size() - (1 << j) + 1));
      for (int i = 0; i < (int)spr[j].size(); ++i) {
        spr[j][i] = min(spr[j - 1][i], spr[j - 1][i + (1 << (j - 1))]);
      }
    }
  }
  T get(int l, int r) {
    int d = 31 - __builtin_clz(r - l + 1);
    return min(spr[d][l], spr[d][r - (1 << d) + 1]);
  }
};
int main() {
  cin.tie(0)->sync_with_stdio(0);
  int n, m, q;
  cin >> n >> m >> q;
  vi v(n), g(n);
  for (int i = 0; i < n; ++i) cin >> v[i], v[i]--;
  for (int i = 0; i < n; ++i) g[v[i]] = v[(i + 1) % n];
  vi a(m);
  for (int i = 0; i < m; ++i) cin >> a[i], a[i]--;
  vector<vi> spr(LOG + 1, vi(m));
  vi nxt(n, -1);
  for (int i = m - 1; i >= 0; --i) {
    nxt[a[i]] = i;
    spr[0][i] = nxt[g[a[i]]];
  }
  for (int j = 0; j < LOG; ++j) {
    for (int i = 0; i < m; ++i) {
      if (spr[j][i] == -1)
        spr[j + 1][i] = -1;
      else
        spr[j + 1][i] = spr[j][spr[j][i]];
    }
  }
  vi res(m);
  for (int i = 0; i < m; ++i) {
    int k = i;
    for (int j = LOG; j >= 0; --j) {
      if ((n - 1) & (1 << j)) {
        k = spr[j][k];
        if (k == -1) break;
      }
    }
    res[i] = k == -1 ? inf : k;
  }
  RMQ<int> rmq(res);
  string ans;
  for (int i = 0; i < q; ++i) {
    int l, r;
    cin >> l >> r;
    --l, --r;
    int a = rmq.get(l, r);
    if (a <= r)
      ans.push_back('1');
    else
      ans.push_back('0');
  }
  cout << ans << '\n';
}
