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 int N = 2e5 + 5, LOG = 20;
int n, m, q, pos[N], p[N], a[N], mn[N][LOG], t[4 * N], least[N];
vector<int> v[N];
void update(int node, int start, int end, int id, int val) {
  if (id < start || id > end) return;
  if (start == end) {
    t[node] = val;
    return;
  }
  int mid = (start + end) / 2;
  update(2 * node, start, mid, id, val);
  update(2 * node + 1, mid + 1, end, id, val);
  t[node] = min(t[2 * node], t[2 * node + 1]);
}
int query(int node, int start, int end, int l, int r) {
  if (r < start || l > end) return m;
  if (start >= l && end <= r) return t[node];
  int mid = (start + end) / 2;
  int p1 = query(2 * node, start, mid, l, r);
  int p2 = query(2 * node + 1, mid + 1, end, l, r);
  return min(p1, p2);
}
int binaryLift(int id, int gap) {
  for (int j = LOG - 1; j >= 0; --j)
    if (gap >= (1 << j)) {
      id = mn[id][j];
      gap -= (1 << j);
    }
  return id;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m >> q;
  for (int i = 0; i < n; ++i) {
    cin >> p[i];
    pos[p[i]] = i;
  }
  for (int i = 0; i < 4 * N; ++i) t[i] = m;
  for (int i = 0; i < m; ++i) {
    cin >> a[i];
    v[a[i]].push_back(i);
  }
  for (int i = 0; i <= n; ++i) v[i].push_back(m);
  if (n != 1) {
    for (int j = 0; j < LOG; ++j) mn[m][j] = m;
    for (int i = 0; i < m; ++i) {
      int id = pos[a[i]];
      int nxt = (id == n - 1) ? p[0] : p[id + 1];
      int nxtId = *lower_bound(v[nxt].begin(), v[nxt].end(), i);
      mn[i][0] = nxtId;
    }
    for (int j = 1; j < LOG; ++j)
      for (int i = 0; i < m; ++i) {
        mn[i][j] = mn[mn[i][j - 1]][j - 1];
      }
    for (int i = 0; i < m; ++i) {
      least[i] = binaryLift(i, n - 1);
    }
    for (int i = 0; i < m; ++i) update(1, 0, m - 1, i, least[i]);
  }
  while (q--) {
    int l, r;
    cin >> l >> r;
    l--;
    r--;
    if (query(1, 0, m - 1, l, r) <= r || n == 1)
      cout << "1";
    else
      cout << "0";
  }
  cout << "\n";
  return 0;
}
