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;
template <typename T>
struct SparseTable {
  const int n, lgn;
  const T id;
  vector<vector<T>> st;
  function<T(T, T)> op;
  SparseTable(const vector<T>& a, function<T(T, T)> f, T identity)
      : n(a.size()), lgn(log2(n) + 2), op(f), id(identity) {
    st.assign(lgn, vector<T>(n));
    for (int i = 0; i < n; ++i) {
      st[0][i] = a[i];
    }
    for (int j = 1; j < lgn; ++j) {
      for (int i = 0; i + (1 << j) - 1 < n; ++i) {
        st[j][i] = op(st[j - 1][i], st[j - 1][i + (1 << (j - 1))]);
      }
    }
  }
  T query(int l, int r) {
    T ans = id;
    for (int msk = r - l + 1, j = 0; msk; msk >>= 1, ++j) {
      if (msk & 1) {
        ans = op(ans, st[j][l]);
        l += 1 << j;
      }
    }
    return ans;
  }
};
constexpr int L = 21;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n, m, q;
  cin >> n >> m >> q;
  vector<int> p(n), a(m), idx(n + 1);
  for (int i = 0; i < n; ++i) {
    cin >> p[i];
    idx[p[i]] = i;
  }
  vector<int> ii(n + 1, -1);
  vector<vector<int>> prv(L, vector<int>(m, -1));
  for (int i = 0; i < m; ++i) {
    cin >> a[i];
    int bef = p[(idx[a[i]] + n - 1) % n];
    if (ii[bef] != -1) {
      prv[0][i] = ii[bef];
    }
    ii[a[i]] = i;
  }
  for (int j = 1; j < L; ++j) {
    for (int i = 0; i < m; ++i) {
      if (prv[j - 1][i] != -1) prv[j][i] = prv[j - 1][prv[j - 1][i]];
    }
  }
  auto get = [&](int u, int x) {
    for (int j = 0; j < L && u != -1; ++j, x >>= 1) {
      if (x & 1) {
        u = prv[j][u];
      }
    }
    return u;
  };
  vector<int> t(m);
  for (int i = 0; i < m; ++i) {
    t[i] = get(i, n - 1);
  }
  SparseTable<int> st(
      t, [](int x, int y) { return max(x, y); }, -1000000000);
  string ans = "";
  while (q--) {
    int l, r;
    cin >> l >> r;
    --l;
    --r;
    ans += (st.query(l, r) >= l ? '1' : '0');
  }
  cout << ans << '\n';
}
