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;
struct segtree {
  int n;
  vector<int> data;
  segtree(int N) {
    n = 1;
    while (n < N) n <<= 1;
    data.assign(n * 2, INT_MAX);
  }
  void insert(int k, int x) {
    k += n;
    while (k) {
      data[k] = min(data[k], x);
      k >>= 1;
    }
  }
  int query(int l, int r) {
    l += n;
    r += n;
    int ret = INT_MAX;
    while (l <= r) {
      if (l % 2 == 1) ret = min(ret, data[l++]);
      if (r % 2 == 0) ret = min(ret, data[r--]);
      l >>= 1;
      r >>= 1;
    }
    return ret;
  }
};
int main() {
  int n, m, q;
  cin >> n >> m >> q;
  vector<int> p(n);
  vector<int> r(n);
  for (int i = 0; i < n; i++) {
    cin >> p[i];
    p[i]--;
    r[p[i]] = i;
  }
  int mx_jump = 1;
  int z = 1;
  while (mx_jump < n) {
    mx_jump <<= 1;
    z++;
  }
  vector<vector<int> > j(z);
  for (int i = 0; i < z; i++) j[i].assign(m, -1);
  vector<int> a(m);
  for (int i = 0; i < m; i++) cin >> a[i];
  vector<int> last(n, -1);
  for (int i = m - 1; i >= 0; i--) {
    int x = a[i] - 1;
    int next = p[(r[x] + 1) % n];
    j[0][i] = last[next];
    last[x] = i;
  }
  for (int i = 1; i < z; i++) {
    for (int k = 0; k < m; k++) {
      if (j[i - 1][k] == -1) {
        j[i][k] = -1;
      } else {
        j[i][k] = j[i - 1][j[i - 1][k]];
      }
    }
  }
  segtree st(m);
  for (int i = 0; i < m; i++) {
    int target = i;
    int z = 0, jump = 1;
    while (jump <= (n - 1)) {
      if (target == -1) break;
      if (jump & (n - 1)) {
        target = j[z][target];
      }
      z++;
      jump <<= 1;
    }
    if (target == -1) {
      target = INT_MAX;
    }
    st.insert(i, target);
  }
  while (q--) {
    int u, v;
    cin >> u >> v;
    u--;
    v--;
    bool ans = st.query(u, v) <= v;
    cout << ans;
  }
  cout << endl;
  return 0;
}
