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;
int per, form, query;
int permu[200005], form_num[200005];
int pre_pos[200005], pre_sub[200005][25];
int pre_per_num[200005];
int pre_end[200005], max_pre_end[200005][25];
void prepare() {
  permu[0] = permu[per];
  for (int i = 1; i <= per; i++) pre_per_num[permu[i]] = permu[i - 1];
  for (int i = 1; i <= form; i++) {
    pre_sub[i][0] = pre_pos[pre_per_num[form_num[i]]];
    pre_pos[form_num[i]] = i;
  }
  for (int gen = 1; gen <= 20; gen++)
    for (int i = 1; i <= form; i++)
      pre_sub[i][gen] = pre_sub[pre_sub[i][gen - 1]][gen - 1];
  for (int i = per; i <= form; i++) {
    int cur = per - 1, cur_pos = i;
    for (int gen = 20; gen >= 0; gen--)
      if (cur >= (1 << gen)) {
        cur_pos = pre_sub[cur_pos][gen], cur -= (1 << gen);
      }
    pre_end[i] = cur_pos;
  }
  for (int i = 1; i <= form; i++) max_pre_end[i][0] = pre_end[i];
  for (int gen = 1; gen <= 20; gen++)
    for (int i = 1; i <= form; i++) {
      int pre = max(i - (1 << (gen - 1)), 0);
      max_pre_end[i][gen] =
          max(max_pre_end[i][gen - 1], max_pre_end[pre][gen - 1]);
    }
}
void solve() {
  prepare();
  for (int i = 1; i <= query; i++) {
    int from, to;
    scanf("%d %d", &from, &to);
    int jump = (int)log2(to - from + 1);
    int cur =
        max(max_pre_end[to][jump], max_pre_end[from + (1 << jump) - 1][jump]);
    if (cur >= from)
      printf("1");
    else
      printf("0");
  }
}
int main() {
  scanf("%d %d %d", &per, &form, &query);
  for (int i = 1; i <= per; i++) scanf("%d", &permu[i]);
  for (int i = 1; i <= form; i++) scanf("%d", &form_num[i]);
  solve();
}
