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 n, m, q;
int p[200001];
int a[200001];
vector<int> cur[200001];
int pos[200001];
int par[200001][21];
struct cmp {
  bool operator()(pair<int, int> a, pair<int, int> b) {
    return a.second > b.second;
  }
};
priority_queue<pair<int, int>, vector<pair<int, int> >, cmp> h;
struct Q {
  int l, r, id;
};
vector<Q> Query;
bool cmp(Q a, Q b) { return a.l < b.l; }
int ans[200001];
int Process(int pos) {
  int k = n - 1;
  for (int i = 20; i >= 0; i--) {
    if (k & (1 << i)) {
      if (par[pos][i] == -1) return -1;
      pos = par[pos][i];
    }
  }
  return pos;
}
int main() {
  cin >> n >> m >> q;
  for (int i = 1; i <= n; i++) {
    cin >> p[i];
    pos[p[i]] = i;
  }
  for (int i = 1; i <= m; i++) {
    cin >> a[i];
  }
  memset(par, -1, sizeof par);
  for (int i = 1; i <= m; i++) {
    int x = pos[a[i]];
    int y;
    if (x == 1)
      y = p[n];
    else
      y = p[x - 1];
    for (auto k : cur[y]) {
      par[k][0] = i;
    }
    cur[y].clear();
    cur[a[i]].push_back(i);
  }
  for (int j = 1; j <= 20; j++) {
    for (int i = 1; i <= m; i++) {
      if (par[i][j - 1] != -1) par[i][j] = par[par[i][j - 1]][j - 1];
    }
  }
  for (int i = 1; i <= q; i++) {
    int l, r;
    cin >> l >> r;
    Query.push_back({l, r, i});
  }
  sort(Query.begin(), Query.end(), cmp);
  for (int i = 1; i <= m; i++) {
    int r = Process(i);
    if (r != -1) h.push({i, r});
  }
  for (auto x : Query) {
    int id = x.id;
    while (!h.empty() && h.top().first < x.l) h.pop();
    if (h.empty() || h.top().second > x.r)
      ans[id] = 0;
    else
      ans[id] = 1;
  }
  for (int i = 1; i <= q; i++) cout << ans[i];
  return 0;
}
