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 = 200005;
template <class T1, class T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &a) {
  return os << '(' << a.first << ", " << a.second << ')';
}
template <class T>
ostream &operator<<(ostream &os, const vector<T> &a) {
  os << '[';
  for (unsigned int i = 0; i < a.size(); i++)
    os << a[i] << (i < a.size() - 1 ? ", " : "");
  os << ']';
  return os;
}
int read() {
  int x;
  cin >> x;
  return x;
}
int len, n, q;
int mask[N];
vector<int> perm;
vector<int> a;
int jump[N][19];
int soonest[N];
int last[N];
int pre(int x) {
  if (x != 1) return x - 1;
  return len;
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> len >> n >> q;
  for (int i = (int)1; i <= (int)len; i++) {
    int t;
    cin >> t;
    mask[t] = i;
  }
  for (int i = (int)1; i <= (int)n; i++) {
    int t;
    cin >> t;
    t = mask[t];
    a.push_back(t);
  }
  memset(last, -1, sizeof(last));
  for (int i = (int)0; i <= (int)n - 1; i++) {
    for (int k = (int)0; k <= (int)18; k++) {
      if (k == 0)
        jump[i][0] = last[pre(a[i])];
      else {
        if (jump[i][k - 1] == -1)
          jump[i][k] = -1;
        else
          jump[i][k] = jump[jump[i][k - 1]][k - 1];
      }
    }
    int &cur = soonest[i];
    cur = i;
    int dis = len - 1;
    for (int k = (int)0; k <= (int)18; k++) {
      if (((dis >> k) & 1LL)) {
        cur = jump[cur][k];
        if (cur == -1) break;
      }
    }
    if (i) soonest[i] = max(soonest[i], soonest[i - 1]);
    last[a[i]] = i;
  }
  for (int i = (int)1; i <= (int)q; i++) {
    int l, r;
    cin >> l >> r;
    l--;
    r--;
    if (soonest[r] >= l)
      cout << 1;
    else
      cout << 0;
  }
}
