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;
int __tag__ = 0;
template <class L, class R>
ostream& operator<<(ostream& out, pair<L, R>& p) {
  return out << p.first << " " << p.second;
}
template <class T>
ostream& operator<<(ostream& out, vector<T>& vec) {
  for (auto it = vec.begin(); it != vec.end(); ++it) {
    out << ((it != begin(vec)) ? " " : "") << *it;
  }
  return out;
}
template <class T, class U>
inline bool chkmax(T& a, U b) {
  return (a < b) ? (a = b, true) : false;
}
template <class T, class U>
inline bool chkmin(T& a, U b) {
  return (a > b) ? (a = b, true) : false;
}
void init();
void solve();
int main(int argc, char** argv) {
  if ((__tag__ = (argc > 1))) {
    assert(freopen(argv[1], "r", stdin));
    cerr.setf(ios_base::fixed), cerr.precision(4);
  }
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int T = 1;
  for (decay<decltype(1)>::type Case = (1), _BOUND = (T + 1); Case < _BOUND;
       Case++) {
    init();
    solve();
  }
  auto times = (clock() * 1.0 / CLOCKS_PER_SEC);
  if (__tag__)
    cerr << "["
            "times"
            ": "
         << times << "]"
         << "\n";
}
const int maxn = 2e5 + 5;
void init() {}
int p[maxn], a[maxn], nxt[maxn][20];
int last[maxn], go[maxn], pos[maxn];
void solve() {
  int n, m, q;
  cin >> n >> m >> q;
  for (decay<decltype(0)>::type i = (0), _BOUND = (n); i < _BOUND; i++) {
    cin >> p[i];
    if (i) go[p[i - 1]] = p[i];
  }
  go[p[n - 1]] = p[0];
  for (decay<decltype(0)>::type i = (0), _BOUND = (m); i < _BOUND; i++)
    cin >> a[i];
  for (decay<decltype(0)>::type j = (0), _BOUND = (20); j < _BOUND; j++)
    nxt[m][j] = m;
  for (decay<decltype(1)>::type i = (1), _BOUND = (n + 1); i < _BOUND; i++)
    last[i] = m;
  for (decay<decltype(m)>::type i = (m)-1, _BOUND = (0); i >= _BOUND; i--) {
    nxt[i][0] = last[go[a[i]]];
    last[a[i]] = i;
    for (decay<decltype(1)>::type j = (1), _BOUND = (20); j < _BOUND; j++) {
      nxt[i][j] = nxt[nxt[i][j - 1]][j - 1];
    }
    int cur = i, len = n - 1;
    for (decay<decltype(20)>::type j = (20) - 1, _BOUND = (0); j >= _BOUND;
         j--) {
      if (len >= (1 << j)) {
        len -= (1 << j), cur = nxt[cur][j];
      }
    }
    pos[i] = cur;
  }
  for (decay<decltype(m - 1)>::type i = (m - 1) - 1, _BOUND = (0); i >= _BOUND;
       i--) {
    chkmin(pos[i], pos[i + 1]);
  }
  while (q--) {
    int l, r;
    cin >> l >> r;
    --l, --r;
    cout << (pos[l] <= r);
  }
  cout << "\n";
}
