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;
using ll = long long;
constexpr int N = 200010;
constexpr int LOGN = 20;
int up[N][LOGN];
int pos[N];
struct SegmentTree {
  SegmentTree(vector<int> a) : n(a.size()) {
    tree.resize(4 * n, -1);
    build(1, 0, n - 1, a);
  }
  void build(int v, int tl, int tr, const vector<int>& a) {
    if (tl == tr) {
      tree[v] = a[tr];
      return;
    }
    int tm = (tl + tr) / 2;
    build(2 * v, tl, tm, a);
    build(2 * v + 1, tm + 1, tr, a);
    tree[v] = max(tree[2 * v], tree[2 * v + 1]);
  }
  int query(int l, int r) const { return query(1, 0, n - 1, l, r); }
  int query(int v, int tl, int tr, int l, int r) const {
    if (l > r) return -1;
    if (tl == l && tr == r) {
      return tree[v];
    }
    int tm = (tl + tr) / 2;
    int ql = query(2 * v, tl, tm, l, min(tm, r));
    int qr = query(2 * v + 1, tm + 1, tr, max(l, tm + 1), r);
    return max(ql, qr);
  }
  vector<int> tree;
  int n;
};
int mp[N];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(nullptr);
  cout.tie(nullptr);
  int n, m, q;
  cin >> m >> n >> q;
  vector<int> p(m);
  for (int i = 0; i < m; ++i) {
    cin >> p[i];
    mp[p[i]] = i;
  }
  vector<int> a(n);
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
  }
  for (int i = 0; i < N; ++i) {
    fill(up[i], up[i] + LOGN, -1);
  }
  fill(pos, pos + N, -1);
  auto prev = [&](const int n) {
    int idx = mp[n];
    --idx;
    if (idx < 0) idx = m - 1;
    return p[idx];
  };
  pos[a[0]] = 0;
  for (int i = 1; i < n; ++i) {
    int from = prev(a[i]);
    if (pos[from] == -1) {
      pos[a[i]] = i;
      continue;
    }
    up[i][0] = pos[from];
    pos[a[i]] = i;
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 1; j < LOGN; ++j) {
      if (up[i][j - 1] >= 0) {
        up[i][j] = up[up[i][j - 1]][j - 1];
      }
    }
  }
  vector<int> b(n, -1);
  for (int i = 0; i < n; ++i) {
    int l = m - 1, to = i;
    for (int j = LOGN - 1; j >= 0; --j) {
      if (l - (1 << j) >= 0) {
        l -= 1 << j;
        to = up[to][j];
        if (to == -1) {
          break;
        }
      }
    }
    b[i] = to;
  }
  SegmentTree tree(move(b));
  auto query = [&tree](const int lo, const int hi) {
    int left = tree.query(lo, hi);
    return (lo <= left) ? 1 : 0;
  };
  while (q-- > 0) {
    int l, r;
    cin >> l >> r;
    --l;
    --r;
    cout << query(l, r);
  }
  cout << endl;
  return 0;
}
