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 MAXVAL = 2e5 + 1;
void next_element(int* next, int n) {
  int p[n];
  for (int i = 0; i < n; ++i) {
    cin >> p[i];
    --p[i];
    if (i) {
      next[p[i - 1]] = p[i];
    }
  }
  next[p[n - 1]] = p[0];
}
void link_table(int* a, int* p, int n, int m, int lnn,
                vector<vector<int> >& table) {
  int next[n];
  for (int i = 0; i < n; ++i) {
    next[i] = MAXVAL;
  }
  for (int i = m - 1; i >= 0; --i) {
    int pair = p[a[i]];
    table[0][i] = next[pair];
    next[a[i]] = i;
  }
  for (int i = 1; i < lnn; ++i) {
    for (int j = 0; j < m; ++j) {
      int firststep = table[i - 1][j];
      if (firststep != MAXVAL) {
        table[i][j] = table[i - 1][firststep];
      } else {
        table[i][j] = MAXVAL;
      }
    }
  }
}
void find_end_pos(int* a, int* p, int n, int m, int* next) {
  int lnn;
  if (n == 1) {
    lnn = 1;
  } else {
    lnn = log2(n - 1) + 1;
  }
  vector<vector<int> > table(lnn, vector<int>(m));
  link_table(a, p, n, m, lnn, table);
  for (int i = 0; i < m; ++i) {
    next[i] = i;
  }
  int shift = n - 1;
  for (int j = 0; j < lnn; ++j) {
    if (shift % 2) {
      for (int i = 0; i < m; ++i) {
        if (next[i] != MAXVAL) {
          next[i] = table[j][next[i]];
        }
      }
    }
    shift /= 2;
  }
}
void build_tree(int* end_pos, int size) {
  for (int i = size - 1; i > 0; --i) {
    end_pos[i] = min(end_pos[i * 2], end_pos[i * 2 + 1]);
  }
}
int l, r;
int find_min_endpos(int* end_pos, int v, int lleaf, int rleaf) {
  if (lleaf >= l && rleaf <= r) {
    return end_pos[v];
  }
  if (r <= lleaf || rleaf <= l) {
    return MAXVAL;
  }
  int mid = (rleaf + lleaf) / 2;
  return min(find_min_endpos(end_pos, 2 * v, lleaf, mid),
             find_min_endpos(end_pos, 2 * v + 1, mid, rleaf));
}
int main() {
  int n, m, q;
  cin >> n >> m >> q;
  int p[n];
  next_element(p, n);
  int a[m];
  for (int i = 0; i < m; ++i) {
    cin >> a[i];
    --a[i];
  }
  int size;
  if (m == 1) {
    size = 1;
  } else {
    size = 1 << int(log2(m - 1) + 1);
  }
  int end_pos[size * 2];
  for (int i = size; i < 2 * size; ++i) {
    end_pos[i] = MAXVAL;
  }
  find_end_pos(a, p, n, m, end_pos + size);
  build_tree(end_pos, size);
  for (; q > 0; --q) {
    cin >> l >> r;
    --l;
    int res = find_min_endpos(end_pos, 1, 0, size);
    if (res < r) {
      cout << "1";
    } else {
      cout << "0";
    }
  }
  cout << endl;
  return 0;
}
