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;
namespace ProconLib {
template <class Monoid>
class SegmentTree {
 public:
  using value_t = typename Monoid::value_t;

 private:
  int N;
  std::vector<value_t> dat;
  static int calcN(int n) {
    int res = 1;
    while (res < n) res *= 2;
    return res;
  }
  value_t queryImpl(int a, int b, int k, int l, int r);

 public:
  SegmentTree(int N);
  void update(int pos, value_t val);
  void updateALL(std::vector<value_t> x);
  value_t query(int a, int b);
};
struct Monoid {
  using value_t = int;
  static constexpr value_t E() { return 1e9; }
  static value_t op(value_t lhs, value_t rhs) { return min(lhs, rhs); }
};
template <typename Monoid>
SegmentTree<Monoid>::SegmentTree(int n)
    : N(calcN(n)), dat(2 * N - 1, Monoid::E()) {}
template <typename Monoid>
void SegmentTree<Monoid>::update(int pos, value_t val) {
  pos += N - 1;
  dat[pos] = val;
  while (pos != 0) {
    int par = (pos - 1) / 2;
    dat[par] = Monoid::op(dat[par * 2 + 1], dat[par * 2 + 2]);
    pos = par;
  }
}
template <typename Monoid>
void SegmentTree<Monoid>::updateALL(std::vector<value_t> x) {
  for (int i = 0; i < x.size(); i++) dat[N - 1 + i] = x[i];
  for (int i = N - 2; i >= 0; i--)
    dat[i] = Monoid::op(dat[i * 2 + 1], dat[i * 2 + 2]);
}
template <typename Monoid>
typename SegmentTree<Monoid>::value_t SegmentTree<Monoid>::query(int a, int b) {
  return queryImpl(a, b, 0, 0, N);
}
template <typename Monoid>
typename SegmentTree<Monoid>::value_t SegmentTree<Monoid>::queryImpl(
    int a, int b, int k, int l, int r) {
  if (a <= l && r <= b) return dat[k];
  if (r <= a || b <= l) return Monoid::E();
  int mid = (l + r) / 2;
  value_t c1v = queryImpl(a, b, k * 2 + 1, l, mid);
  value_t c2v = queryImpl(a, b, k * 2 + 2, mid, r);
  return Monoid::op(c1v, c2v);
}
}  // namespace ProconLib
const int logN = 20;
int main() {
  int n, m, q;
  cin >> n >> m >> q;
  vector<int> p(n);
  for (int i = 0; i < n; i++) cin >> p[i], p[i]--;
  vector<int> a(m);
  for (int i = 0; i < m; i++) cin >> a[i], a[i]--;
  vector<int> nex(n);
  for (int i = 0; i < n; i++) nex[p[i]] = p[(i + 1) % n];
  vector<int> pos(n, m);
  vector<vector<int>> step(logN, vector<int>(m + 1, m));
  for (int i = m - 1; i >= 0; i--) {
    pos[a[i]] = i;
    step[0][i] = pos[nex[a[i]]];
  }
  for (int i = 0; i + 1 < logN; i++) {
    for (int j = 0; j <= m; j++) {
      step[i + 1][j] = step[i][step[i][j]];
    }
  }
  vector<int> vec(m);
  for (int i = 0; i < m; i++) {
    int x = n - 1;
    int p = i;
    for (int j = logN - 1; j >= 0; j--) {
      if ((x >> j) & 1) {
        p = step[j][p];
      }
    }
    vec[i] = p;
  }
  ProconLib::SegmentTree<ProconLib::Monoid> seg(m);
  seg.updateALL(vec);
  vector<int> res(q);
  for (int i = 0; i < q; i++) {
    int l, r;
    cin >> l >> r;
    l--;
    res[i] = (seg.query(l, r) < r);
  }
  for (int i = 0; i < q; i++) cout << res[i];
  cout << endl;
  return 0;
}
