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;
long long n, m, q;
vector<long long> a, p, rp;
vector<vector<long long>> b;
int main() {
  cin >> n >> m >> q;
  p.resize(n);
  a.resize(m);
  b.resize(m);
  rp.resize(n + 1, 0);
  for (int(i) = 0; (i) < (m); ++(i)) b[i].resize(20, -1);
  for (int(i) = 0; (i) < (n); ++(i)) cin >> p[i];
  for (int(i) = 0; (i) < (m); ++(i)) cin >> a[i];
  for (int(i) = 0; (i) < (n); ++(i)) rp[p[i]] = i;
  vector<int> lastPos;
  lastPos.resize(n + 1, -1);
  for (int i = 0; i < m; ++i) {
    if (a[i] >= 1 && a[i] <= n) {
      lastPos[a[i]] = i;
      int prev = rp[a[i]] - 1;
      if (prev == -1) prev = n - 1;
      b[i][0] = lastPos[p[prev]];
    }
  }
  for (int j = 0; j < 20; ++j) {
    for (int i = 0; i < m; ++i) {
      int t = b[i][j];
      if (t >= 0) {
        t = b[t][j];
        b[i][j + 1] = t;
      }
    }
  }
  vector<int> bn_1;
  bn_1.resize(m, -1);
  for (int(i) = 0; (i) < (m); ++(i)) {
    int rem = n - 1;
    int j = 20;
    int ans = i;
    while (rem > 0 && ans >= 0) {
      while (((rem >> j) & 1) == 0) --j;
      ans = b[ans][j];
      rem -= (1 << j);
    }
    bn_1[i] = ans;
  }
  for (int i = 1; i < m; ++i) {
    bn_1[i] = max(bn_1[i], bn_1[i - 1]);
  }
  for (int(i) = 0; (i) < (q); ++(i)) {
    long long l, r;
    cin >> l >> r;
    --l;
    --r;
    if (bn_1[r] >= l)
      cout << 1;
    else
      cout << 0;
  }
  cout << endl;
  return 0;
}
