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 N = 2e5 + 7;
int dp1[N], dpn[N], p[N], v[N];
vector<int> pozitii[N], updates[N];
vector<pair<int, int> > queries[N];
bool ans[N];
int n, m;
int cb(int val, int poz) {
  int pas(1 << 17), r(-1);
  while (pas) {
    if (r + pas < pozitii[val].size() && pozitii[val][r + pas] < poz) r += pas;
    pas >>= 1;
  }
  return r;
}
void precalc() {
  for (int i = 1; i <= m; ++i) pozitii[v[i]].push_back(i);
  for (int i = 1; i <= m; ++i) {
    if (v[i] == 1) {
      dp1[i] = i;
      continue;
    }
    if (pozitii[v[i] - 1].size() == 0 || pozitii[v[i] - 1].front() > i) {
      dp1[i] = -1;
      continue;
    }
    int p = cb(v[i] - 1, i);
    assert(p != -1);
    dp1[i] = dp1[pozitii[v[i] - 1][p]];
  }
  for (int i = m; i >= 1; --i) {
    if (v[i] == n) {
      dpn[i] = i;
      continue;
    }
    if (pozitii[v[i] + 1].size() == 0 || pozitii[v[i] + 1].back() < i) {
      dpn[i] = -1;
      continue;
    }
    int p = cb(v[i] + 1, i);
    dpn[i] = dpn[pozitii[v[i] + 1][p + 1]];
  }
  for (int i = 1; i <= m; ++i) {
    int x = dp1[i];
    if (dp1[i] == -1) continue;
    if (v[i] == n) {
      updates[x].push_back(i);
      continue;
    }
    int pas = 1 << 17, r(-1);
    while (pas) {
      if (r + pas < pozitii[v[i] + 1].size() &&
          dpn[pozitii[v[i] + 1][r + pas]] != -1 &&
          dpn[pozitii[v[i] + 1][r + pas]] < x)
        r += pas;
      pas >>= 1;
    }
    if (r != -1) updates[pozitii[v[i] + 1][r]].push_back(i);
  }
}
void solve() {
  int cur(1e9);
  for (int i = m; i >= 1; --i) {
    for (auto j : updates[i]) cur = min(cur, j);
    for (auto j : queries[i])
      if (cur <= j.first) ans[j.second] = 1;
  }
}
int main() {
  int q, val;
  cin >> n >> m >> q;
  for (int i = 1; i <= n; ++i) cin >> val, p[val] = i;
  for (int i = 1; i <= m; ++i) {
    cin >> v[i];
    v[i] = p[v[i]];
  }
  precalc();
  int st, dr;
  for (int i = 1; i <= q; ++i) {
    cin >> st >> dr;
    queries[st].push_back({dr, i});
  }
  solve();
  for (int i = 1; i <= q; ++i) cout << ans[i];
  return 0;
}
