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;
const int maxLog = 20;
vector<int> last, perm, arr, lastPos, point[maxLog], vec;
int n, m, q, l, r, k;
struct RMQ;
inline int getN(int ind) {
  int res = ind;
  for (int i = 0; i < maxLog; i++) {
    if ((1LL << i) & (n - 1)) res = point[i][res];
    if (res == -1) return -1;
  }
  return res;
}
struct RMQ {
  vector<int> sparse[maxLog];
  RMQ() {}
  RMQ(vector<int> arr) {
    for (int i = 0; i < maxLog; i++) sparse[i].resize(arr.size() + 5);
    for (int i = 0; i < arr.size(); i++) {
      sparse[0][i] = arr[i];
    }
    for (int i = 1; i < maxLog; i++) {
      if ((1LL << i) >= arr.size()) break;
      for (int j = 0; j <= arr.size() - (1LL << i); j++) {
        sparse[i][j] =
            max(sparse[i - 1][j], sparse[i - 1][j + (1LL << (i - 1))]);
      }
    }
  }
  int query(int l, int r) {
    int len = r - l, k;
    for (k = 0; k < len; k++) {
      if ((1LL << k) <= len && (1LL << (k + 1)) > len) break;
    }
    return max(sparse[k][l], sparse[k][r - (1LL << k)]);
  }
} rmq;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  ;
  cin >> n >> m >> q;
  last.resize(n);
  lastPos.resize(n);
  perm.resize(n);
  arr.resize(m);
  vec.resize(m);
  fill(lastPos.begin(), lastPos.end(), -1);
  for (int i = 0; i < maxLog; i++) {
    point[i].resize(m);
  }
  for (int i = 0; i < n; i++) {
    cin >> perm[i];
    perm[i]--;
  }
  for (int i = 0; i < n; i++) {
    last[perm[i]] = perm[(i + n - 1) % n];
  }
  for (int i = 0; i < m; i++) {
    cin >> arr[i];
    arr[i]--;
    if (lastPos[last[arr[i]]] == -1) {
      for (int j = 0; j < maxLog; j++) {
        point[j][i] = -1;
      }
    } else {
      point[0][i] = lastPos[last[arr[i]]];
      for (int j = 1; j < maxLog; j++) {
        if (point[j - 1][i] == -1) {
          point[j][i] = -1;
          continue;
        }
        point[j][i] = point[j - 1][point[j - 1][i]];
      }
    }
    vec[i] = getN(i);
    lastPos[arr[i]] = i;
  }
  rmq = RMQ(vec);
  while (q--) {
    cin >> l >> r;
    l--;
    cout << (rmq.query(l, r) >= l);
  }
}
