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 double EPS = 1e-9;
struct SegmentTree {
 private:
  long long n;
  vector<long long> node;

 public:
  SegmentTree(vector<long long> v) {
    long long sz = (long long)v.size();
    n = 1;
    while (n < sz) n *= 2;
    node.resize(2 * n - 1);
    for (long long i = (0); i < (sz); i++) node[i + n - 1] = v[i];
    for (long long i = (n - 1 - 1); i >= 0; i--)
      node[i] = min(node[i * 2 + 1], node[i * 2 + 2]);
  }
  void update(long long k, long long a) {
    k += n - 1;
    node[k] = a;
    while (k > 0) {
      k = (k - 1) / 2;
      node[k] = min(node[k * 2 + 1], node[k * 2 + 2]);
    }
  }
  long long query(long long a, long long b, long long k = 0, long long l = 0,
                  long long r = -1) {
    if (r < 0) r = n;
    if (r <= a || b <= l) return (1LL << 60);
    if (a <= l && r <= b)
      return node[k];
    else {
      long long vl = query(a, b, k * 2 + 1, l, (l + r) / 2);
      long long vr = query(a, b, k * 2 + 2, (l + r) / 2, r);
      return min(vl, vr);
    }
  }
};
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  long long n, m, q;
  cin >> n >> m >> q;
  vector<long long> p(n);
  for (long long i = (0); i < (n); i++) cin >> p[i];
  vector<long long> a(m);
  for (long long i = (0); i < (m); i++) cin >> a[i];
  vector<long long> fol(n + 1);
  for (long long i = (0); i < (n); i++) fol[p[i]] = p[(i + 1) % n];
  long long d = log2(n) + 1;
  vector<vector<long long>> next(m, vector<long long>(d, (1LL << 60)));
  vector<long long> id(n + 1, (1LL << 60));
  for (long long i = (m - 1); i >= 0; i--) {
    id[a[i]] = i;
    next[i][0] = id[fol[a[i]]];
  }
  for (long long i = (1); i < (d); i++) {
    for (long long j = (0); j < (m); j++) {
      long long in = j;
      for (long long _ = (0); _ < (2); _++)
        if (in != (1LL << 60)) in = next[in][i - 1];
      next[j][i] = in;
    }
  }
  vector<long long> tmp(m);
  for (long long i = (0); i < (m); i++) {
    long long cur = i, sum = 0;
    for (long long j = (d - 1); j >= 0; j--) {
      if (sum + pow(2, j) > n - 1) continue;
      if (cur == (1LL << 60)) break;
      cur = next[cur][j];
      sum += pow(2, j);
    }
    tmp[i] = cur;
  }
  SegmentTree seg(tmp);
  for (long long _ = (0); _ < (q); _++) {
    long long l, r;
    cin >> l >> r;
    if (seg.query(l - 1, r) < r)
      cout << 1;
    else
      cout << 0;
  }
  cout << endl;
  return 0;
}
