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 RMQ {
  vector<vector<int>> table;
  RMQ() {}
  RMQ(vector<int>& v) {
    int n = (int)v.size();
    int lg = 32 - __builtin_clz(n);
    table = vector<vector<int>>(lg, vector<int>(n));
    for (int i = 0; i < n; i++) table[0][i] = v[i];
    for (int k = 1, len = 1; k < lg; k++, len <<= 1)
      for (int i = 0; i < n; i++)
        table[k][i] = min(table[k - 1][i], table[k - 1][min(i + len, n - 1)]);
  }
  int query(const int& a, const int& b) {
    int e = 1 << (31 - __builtin_clz(b - a + 1));
    int k = __builtin_ctz(e);
    return min(table[k][a], table[k][b - e + 1]);
  }
};
void sol() {
  int N, M, Q;
  cin >> N >> M >> Q;
  vector<int> perm(N), loc(N);
  for (int i = 0; i < N; i++) {
    cin >> perm[i];
    perm[i]--;
    loc[perm[i]] = i;
  }
  vector<int> nums(M);
  for (int i = 0; i < M; i++) {
    cin >> nums[i];
    nums[i]--;
  }
  vector<int> last(N, M), ptsTo(M, M);
  for (int i = M - 1; i >= 0; i--) {
    int pos = (loc[nums[i]] + 1) % N;
    int who = perm[pos];
    ptsTo[i] = last[who];
    assert(ptsTo[i] > i);
    last[nums[i]] = i;
  }
  int LG = 1;
  while (1 << LG <= M) LG++;
  vector<vector<int>> lft(LG, vector<int>(M + 1));
  for (int i = 0; i < M; i++) lft[0][i] = ptsTo[i];
  lft[0][M] = M;
  for (int lg = 1; lg < LG; lg++) {
    for (int i = 0; i <= M; i++) {
      lft[lg][i] = lft[lg - 1][lft[lg - 1][i]];
    }
  }
  vector<int> arr(M);
  for (int i = 0; i < M; i++) {
    int moves = N - 1, to = i;
    for (int j = LG - 1; j >= 0; j--)
      if (1 << j <= moves) {
        to = lft[j][to];
        moves -= 1 << j;
      }
    arr[i] = to;
  }
  RMQ rmq(arr);
  while (Q--) {
    int L, R;
    cin >> L >> R;
    L--;
    R--;
    int it = rmq.query(L, R);
    if (it > R)
      cout << "0";
    else
      cout << "1";
  }
  cout << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  sol();
  return 0;
}
