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 long long mod = 1000000007;
const long long INF = mod * mod;
const long double eps = 1e-8;
const long double pi = acos(-1.0);
struct SegT {
 private:
  int sz;
  vector<int> node;
  const int init_c = mod;

 public:
  SegT(vector<int> c) {
    int n = c.size();
    sz = 1;
    while (sz < n) sz *= 2;
    node.resize(2 * sz - 1, init_c);
    for (int i = 0; i < n; i++) {
      node[sz - 1 + i] = c[i];
    }
    for (int i = sz - 1 - 1; i >= 0; i--) {
      node[i] = f(node[2 * i + 1], node[2 * i + 2]);
    }
  }
  int f(int a, int b) { return min(a, b); }
  void update(int k, int a) {
    k += sz - 1;
    node[k] = a;
    while (k > 0) {
      k = (k - 1) / 2;
      node[k] = f(node[k * 2 + 1], node[k * 2 + 2]);
    }
  }
  int query(int a, int b, int k = 0, int l = 0, int r = -1) {
    if (r < 0) r = sz;
    if (r <= a || b <= l)
      return init_c;
    else if (a <= l && r <= b)
      return node[k];
    else {
      int vl = query(a, b, k * 2 + 1, l, (l + r) / 2);
      int vr = query(a, b, k * 2 + 2, (l + r) / 2, r);
      return f(vl, vr);
    }
  }
};
int par[1 << 18][18];
vector<int> loc[1 << 18];
void solve() {
  int n, m, q;
  cin >> n >> m >> q;
  vector<int> p(n), invp(n);
  for (int i = 0; i < n; i++) {
    cin >> p[i];
    p[i]--;
    invp[p[i]] = i;
  }
  vector<int> a(m);
  for (int i = 0; i < m; i++) {
    cin >> a[i];
    a[i]--;
    loc[a[i]].push_back(i);
  }
  for (int i = 0; i < n; i++) loc[i].push_back(m);
  for (int i = 0; i < m; i++) {
    int z = invp[a[i]];
    z++;
    if (z == n) z = 0;
    z = p[z];
    int id = upper_bound(loc[z].begin(), loc[z].end(), i) - loc[z].begin();
    par[i][0] = loc[z][id];
  }
  for (int i = 0; i < 18; i++) par[m][i] = m;
  for (int i = 1; i <= 17; i++) {
    for (int j = 0; j < m; j++) {
      par[j][i] = par[par[j][i - 1]][i - 1];
    }
  }
  vector<int> v;
  for (int i = 0; i < 18; i++) {
    if ((n - 1) & (1 << i)) {
      v.push_back(i);
    }
  }
  vector<int> ri(m);
  for (int i = 0; i < m; i++) {
    int cur = i;
    for (int j = 0; j < v.size(); j++) {
      cur = par[cur][v[j]];
    }
    ri[i] = cur;
  }
  SegT st(ri);
  string ans;
  for (int i = 0; i < q; i++) {
    int l, r;
    cin >> l >> r;
    l--;
    r--;
    int u = st.query(l, r + 1);
    if (r < u)
      ans.push_back('0');
    else
      ans.push_back('1');
  }
  cout << ans << endl;
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  solve();
  return 0;
}
