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 st[200010][30];
int nxt[200010];
vector<int> go[200010];
int arr[200010];
vector<int>::iterator it;
int st2[200010][30];
int main() {
  int n, m, q, prev, cur;
  cin >> n >> m >> q;
  cin >> prev;
  int beg = prev;
  for (int i = 0; i < 200005; i++) {
    for (int j = 0; j < 28; j++) st[i][j] = st2[i][j] = INT_MAX;
  }
  for (int i = 1; i < n; ++i) {
    cin >> cur;
    nxt[prev] = cur;
    prev = cur;
  }
  nxt[cur] = beg;
  for (int i = 0; i < m; ++i) {
    cin >> cur;
    arr[i] = cur;
    go[cur].push_back(i);
  }
  for (int i = 0; i < m; ++i) {
    if (go[nxt[arr[i]]].size() == 0) continue;
    it = upper_bound(go[nxt[arr[i]]].begin(), go[nxt[arr[i]]].end(), i);
    int id = it - go[nxt[arr[i]]].begin();
    if (id >= go[nxt[arr[i]]].size()) continue;
    st[i][0] = go[nxt[arr[i]]][id];
  }
  for (int i = m - 1; i >= 0; --i) {
    for (int j = 1; j <= 25; ++j) {
      if (st[i][j - 1] != INT_MAX) st[i][j] = st[st[i][j - 1]][j - 1];
    }
  }
  for (int i = m - 1; i >= 0; --i) {
    int node = i;
    for (int j = 25; j >= 0; --j) {
      if ((n - 1) & (1 << j)) {
        node = st[node][j];
        if (node == INT_MAX) break;
      }
    }
    if (node == INT_MAX) continue;
    st2[i][0] = node;
  }
  for (int i = m - 1; i >= 0; --i) {
    for (int j = 1; j <= 25; ++j) {
      if ((i + (1 << (j - 1))) <= m - 1)
        st2[i][j] = min(st2[i][j - 1], st2[i + (1 << (j - 1))][j - 1]);
    }
  }
  for (int i = 0; i < q; ++i) {
    cin >> prev >> cur;
    prev--;
    cur--;
    int dist = cur - prev + 1;
    int node = prev;
    int mn = INT_MAX;
    for (int j = 25; j >= 0; --j) {
      if (dist & (1 << j)) {
        mn = min(mn, st2[node][j]);
        node = node + (1 << (j));
        if (node >= m) break;
      }
    }
    if (mn <= cur)
      cout << '1';
    else
      cout << '0';
  }
}
