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 MOD = 1e9 + 7;
class SegmentTreeMin {
 public:
  int n;
  vector<long long> vect;
  SegmentTreeMin(int _n) : n(_n) {
    vect.resize(2 * n);
    fill(vect.begin(), vect.end(), 1e10);
  }
  void modify(int p, long long value) {
    for (vect[p += n] = value; p > 1; p >>= 1) {
      vect[p >> 1] = min(vect[p], vect[p ^ 1]);
    }
  }
  long long query(int l, int r) {
    long long res = 1e10;
    for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
      if (l & 1) res = min(res, vect[l++]);
      if (r & 1) res = min(res, vect[--r]);
    }
    return res;
  }
};
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n, m, q;
  cin >> n >> m >> q;
  vector<int> p(n + 1), a(m + 1);
  vector<vector<int>> gr(n + 1);
  for (int i = 1; i <= n; i++) {
    cin >> p[i];
  }
  for (int i = 1; i <= m; i++) {
    cin >> a[i];
    gr[a[i]].push_back(i);
  }
  int th = 200;
  if (n <= th) {
    SegmentTreeMin st(m + 1);
    for (int i = 1; i <= n; i++) {
      for (int j : gr[p[i]]) {
        int next = i + 1 <= n ? i + 1 : 1;
        int curPos = j;
        while (next != i) {
          auto it = lower_bound(gr[p[next]].begin(), gr[p[next]].end(), curPos);
          if (it == gr[p[next]].end()) break;
          curPos = *it;
          next++;
          if (next > n) next = 1;
        }
        if (next == i) st.modify(j, curPos);
      }
    }
    for (int i = 0; i < q; i++) {
      int l, r;
      cin >> l >> r;
      auto a = st.query(l, r + 1);
      cout << (a <= r ? 1 : 0);
    }
    return 0;
  }
  int spos = 1;
  for (int i = 1; i <= n; i++) {
    if (gr[p[i]].size() < gr[p[spos]].size()) spos = i;
  }
  vector<vector<int>> bf(gr[p[spos]].size(), vector<int>(m + 1));
  for (int i = 0; i < gr[p[spos]].size(); i++) {
    int x = gr[p[spos]][i];
    bf[i][x] = 1;
    int gpos = spos + 1;
    if (gpos > n) gpos = 1;
    for (int j = x + 1; j <= m; j++) {
      bf[i][j] = bf[i][j - 1];
      if (a[j] == p[gpos]) {
        bf[i][j]++;
        gpos++;
        if (gpos > n) gpos = 1;
      }
    }
    gpos = spos - 1;
    if (gpos < 1) gpos = n;
    for (int j = x - 1; j >= 1; j--) {
      bf[i][j] = bf[i][j + 1];
      if (a[j] == p[gpos]) {
        bf[i][j]++;
        gpos--;
        if (gpos < 1) gpos = n;
      }
    }
  }
  for (int i = 0; i < q; i++) {
    int l, r;
    cin >> l >> r;
    bool found = 0;
    for (int j = 0; j < gr[p[spos]].size(); j++) {
      if (gr[p[spos]][j] >= l && gr[p[spos]][j] <= r &&
          bf[j][l] + bf[j][r] - 1 >= n) {
        found = 1;
        break;
      }
    }
    cout << found;
  }
}
