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;
class SegTree {
 private:
  int tree[(1 << 19)];

 public:
  SegTree(int N) {
    for (int i = 0; i < (1 << 19); i++) tree[i] = 200005;
  }
  int get_val(int l, int r, int a, int b, int ind) {
    if (a <= l && r <= b) {
      return (tree[ind]);
    }
    if (a > r || b < l) {
      return (200005);
    }
    int leftS = get_val(l, (l + r) / 2, a, b, 2 * ind);
    int rightS = get_val((l + r) / 2 + 1, r, a, b, 2 * ind + 1);
    return (min(leftS, rightS));
  }
  int query(int a, int b) { return (get_val(0, 200005, a, b, 1)); }
  void change_val(int l, int r, int newVal, int ind, int tmp) {
    if (tmp > r || tmp < l) {
      return;
    }
    if (l == r) {
      tree[ind] = newVal;
      return;
    }
    change_val(l, (r + l) / 2, newVal, 2 * ind, tmp);
    change_val((r + l) / 2 + 1, r, newVal, 2 * ind + 1, tmp);
    tree[ind] = min(tree[2 * ind], tree[2 * ind + 1]);
  }
  void update(int ind, int val) { change_val(0, 200005, val, 1, ind); }
};
int bin[200005 + 5][22], perm[200005], nxt[200005], ar[200005], recent[200005],
    ans[200005];
int N, M, Q;
int main() {
  cin >> N >> M >> Q;
  for (int i = 0; i < N; i++) {
    cin >> perm[i];
    recent[i + 1] = 200005;
    if (i > 0) nxt[perm[i - 1]] = perm[i];
  }
  nxt[perm[N - 1]] = perm[0];
  for (int i = 0; i < M; i++) cin >> ar[i];
  for (int i = 0; i <= 200005; i++)
    for (int j = 0; j <= 20; j++) bin[i][j] = 200005;
  for (int i = M - 1; i >= 0; i--) {
    bin[i][0] = i;
    bin[i][1] = recent[nxt[ar[i]]];
    recent[ar[i]] = i;
  }
  for (int ii = 2; ii <= 20; ii++) {
    for (int i = 0; i < M; i++) bin[i][ii] = bin[bin[i][ii - 1]][ii - 1];
  }
  for (int i = 0; i < M; i++) {
    ans[i] = i;
    int sum = N - 1;
    for (int j = 19; j >= 0; j--) {
      if (sum >= (1 << j)) {
        ans[i] = bin[ans[i]][j + 1];
        sum -= (1 << j);
      }
    }
  }
  SegTree seg(200005);
  for (int i = 0; i < M; i++) seg.update(i, ans[i]);
  string str = "";
  int l, r;
  for (int i = 0; i < Q; i++) {
    cin >> l >> r;
    l--;
    r--;
    str += ((seg.query(l, r) <= r) ? "1" : "0");
  }
  cout << str << endl;
  return (0);
}
