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 BF(vector<int> &P, vector<int> &A, int s, int e) {
  for (int i = 0; i < P.size(); ++i) {
    int c = 0;
    for (int j = s; j <= e && c < P.size(); ++j) {
      if (P[(i + c) % P.size()] == A[j]) {
        c++;
      }
    }
    if (c == P.size()) return 1;
  }
  return 0;
}
vector<vector<int> > adj;
void go(int u, int lvl, int N, vector<int> &ST, vector<int> &TT) {
  TT.push_back(u);
  if (lvl >= N) ST[u] = TT[lvl - N];
  for (int v : adj[u]) {
    go(v, lvl + 1, N, ST, TT);
  }
  TT.pop_back();
}
int main() {
  int N, M, Q;
  cin >> N >> M >> Q;
  vector<int> P(N), IP(N), A(M);
  for (int i = 0; i < N; ++i) {
    cin >> P[i];
    P[i]--;
  }
  for (int i = 0; i < N; ++i) {
    IP[P[i]] = i;
  }
  for (int i = 0; i < M; ++i) {
    cin >> A[i];
    A[i]--;
  }
  map<int, int> LAST_SEEN;
  auto getP = [&](int p) { return p == 0 ? P.back() : P[p - 1]; };
  vector<int> IND(M, 0);
  adj = vector<vector<int> >(M);
  for (int i = 0; i < M; ++i) {
    int pv = getP(IP[A[i]]);
    if (!LAST_SEEN.count(pv)) {
    } else {
      int pp = LAST_SEEN[pv];
      adj[pp].push_back(i);
      IND[i] = 1;
    }
    LAST_SEEN[A[i]] = i;
  }
  vector<int> ST(M, -1);
  for (int i = 0; i < M; ++i) {
    if (IND[i] == 0) {
      vector<int> TMP;
      go(i, 1, N, ST, TMP);
    }
  }
  for (int i = 1; i < M; ++i) {
    ST[i] = max(ST[i], ST[i - 1]);
  }
  for (int i = 0; i < Q; ++i) {
    int l, r;
    cin >> l >> r;
    l--;
    r--;
    cout << (ST[r] >= l ? 1 : 0);
  }
  cout << endl;
  return 0;
}
