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;
template <class T, class U>
void ckmin(T &a, U b) {
  if (a > b) a = b;
}
template <class T, class U>
void ckmax(T &a, U b) {
  if (a < b) a = b;
}
int N, M, Q;
int A[200013], B[200013];
int edge[200013], dp[200013], rt[200013];
int lst[200013], need[200013];
int jump[20][200013];
int table[20][200013];
int qry(int L, int R) {
  int sz = 31 - __builtin_clz(R - L + 1);
  return min(table[sz][L], table[sz][R - (1 << sz) + 1]);
}
int32_t main() {
  cout << fixed << setprecision(12);
  cerr << fixed << setprecision(4);
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cin >> N >> M >> Q;
  for (auto i = (0); i < (N); i++) {
    cin >> A[i];
    A[i]--;
  }
  for (auto i = (0); i < (M); i++) {
    cin >> B[i];
    B[i]--;
  }
  for (auto i = (0); i < (N - 1); i++) {
    edge[A[i]] = A[i + 1];
  }
  edge[A[N - 1]] = A[0];
  for (auto i = (0); i < (N); i++) {
    lst[i] = M;
  }
  for (auto i = (M)-1; i >= (0); i--) {
    rt[i] = lst[edge[B[i]]];
    lst[B[i]] = i;
  }
  rt[M] = M;
  for (auto i = (0); i < (M + 1); i++) {
    jump[0][i] = rt[i];
  }
  for (auto i = (1); i < (20); i++) {
    for (auto j = (0); j < (M + 1); j++) {
      jump[i][j] = jump[i - 1][jump[i - 1][j]];
    }
  }
  for (auto i = (0); i < (M); i++) {
    int u = i;
    for (auto j = (20) - 1; j >= (0); j--) {
      if ((N - 1) & (1 << j)) {
        u = jump[j][u];
      }
    }
    dp[i] = u;
  }
  for (auto i = (0); i < (M); i++) {
    table[0][i] = dp[i];
  }
  for (auto i = (1); i < (20); i++) {
    for (auto j = (0); j < (M - (1 << i) + 1); j++) {
      table[i][j] = min(table[i - 1][j], table[i - 1][j + (1 << (i - 1))]);
    }
  }
  while (Q--) {
    int L, R;
    cin >> L >> R;
    L--;
    R--;
    cout << ((qry(L, R) <= R) ? 1 : 0);
  }
  cout << '\n';
  return 0;
}
