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>
struct tree {
  int *arr;
  int _pow = 1;
  void init(int n, int *a) {
    while (_pow < n) {
      _pow *= 2;
    }
    arr = new int[2 * _pow]();
    for (int i = 0; i < n; i++) {
      arr[i + _pow] = a[i];
    }
    int po = _pow / 2;
    while (po > 0) {
      for (int i = 0; i < po; i++) {
        arr[i + po] = std::max(arr[2 * i + 2 * po], arr[2 * i + 2 * po + 1]);
      }
      po /= 2;
    }
  }
  int get(int v, int tl, int tr, int l, int r) {
    if (tl == l && tr == r) {
      return arr[v];
    }
    int m = tl + (tr - tl) / 2;
    if (m < l) {
      return get(2 * v + 1, m + 1, tr, l, r);
    }
    if (m >= r) {
      return get(2 * v, tl, m, l, r);
    }
    return std::max(get(2 * v, tl, m, l, m),
                    get(2 * v + 1, m + 1, tr, m + 1, r));
  }
};
int main() {
  int n, m, k;
  scanf("%d%d%d", &n, &m, &k);
  int log = 0;
  while ((1 << log) <= n) {
    log++;
  }
  int p[n], p1[n], a[m];
  for (int i = 0; i < n; i++) {
    scanf("%d", &p[i]);
    p[i]--;
    p1[p[i]] = i;
  }
  std::set<int> s[n];
  for (int i = 0; i < m; i++) {
    scanf("%d", &a[i]);
    a[i]--;
    s[a[i]].insert(-i);
  }
  int dp[log][m];
  for (int i = 0; i < m; i++) {
    dp[0][i] = i;
  }
  for (int _ = 1; _ < log; _++) {
    for (int i = 0; i < m; i++) {
      if (dp[_ - 1][i] < (1 << (_ - 1))) {
        dp[_][i] = -1;
        continue;
      }
      int val = p1[a[i]] - (1 << (_ - 1));
      if (val < 0) {
        val += n;
      }
      val = p[val];
      std::set<int>::iterator it = s[val].lower_bound(1 - dp[_ - 1][i]);
      if (it == s[val].end()) {
        dp[_][i] = -1;
        continue;
      }
      dp[_][i] = dp[_ - 1][-*it];
    }
  }
  int bou[m];
  for (int i = 0; i < m; i++) {
    bou[i] = i;
    for (int j = log - 1; j >= 0 && bou[i] != -1; j--) {
      if ((n - 1) & (1 << j)) {
        int val = p1[a[bou[i]]] - 1;
        if (val < 0) {
          val += n;
        }
        val = p[val];
        std::set<int>::iterator it = s[val].lower_bound(1 - bou[i]);
        if (it == s[val].end()) {
          bou[i] = -1;
        } else {
          bou[i] = dp[j][-*it];
        }
      }
    }
  }
  tree t;
  t.init(m, bou);
  for (int i = 0; i < k; i++) {
    int l, r;
    scanf("%d%d", &l, &r);
    printf("%d", t.get(1, 1, t._pow, l, r) >= l - 1);
  }
  return 0;
}
