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;
istream& in = cin;
int n, m, q;
int a[200010];
int b[200010];
pair<pair<int, int>, int> Q[200010];
inline int get_ne(int _p) {
  if (_p == n) {
    return 1;
  } else {
    return _p + 1;
  }
}
inline int get_pe(int _p) {
  if (_p == 1) {
    return n;
  } else {
    return _p - 1;
  }
}
int ne[200010];
int pe[200010];
void input() {
  in >> n >> m >> q;
  for (int i = 1; i <= n; ++i) {
    in >> a[i];
  }
  for (int i = 1; i <= m; ++i) {
    in >> b[i];
  }
  for (int i = 1; i <= q; ++i) {
    in >> Q[i].first.first >> Q[i].first.second;
    Q[i].second = i - 1;
  }
}
vector<int> edge[200010];
int dp[200010];
vector<int> ret;
int h[200010];
int E[200010];
bool cmp(pair<pair<int, int>, int> p1, pair<pair<int, int>, int> p2) {
  if (p1.first.first != p2.first.first)
    return p1.first.first > p2.first.first;
  else if (p1.first.second != p2.first.second)
    return p1.first.second > p2.first.second;
  else {
    return p1.second < p2.second;
  }
}
vector<int> path;
bool vis[200010];
void dfs(int p) {
  if (p == 3) {
    int t = 0;
  }
  if (vis[p]) return;
  vis[p] = 1;
  path.push_back(p);
  if (path.size() >= n) {
    E[p] = path[path.size() - n];
  }
  for (int son : edge[p]) {
    dfs(son);
  }
  path.pop_back();
}
int main() {
  ret.resize(200010);
  int TEST_CASE = 1;
  while (TEST_CASE-- > 0) {
    input();
    for (int i = 1; i <= m; ++i) {
      edge[i].clear();
      E[i] = 1e7;
      dp[i] = -1;
    }
    for (int i = 1; i <= n; ++i) {
      ne[a[i]] = a[get_ne(i)];
      pe[a[i]] = a[get_pe(i)];
    }
    for (int i = m; i >= 1; --i) {
      h[b[i]] = i;
      int pp = ne[b[i]];
      if (h[pp]) {
        edge[h[pp]].push_back(i);
      }
    }
    for (int i = m; i >= 1; --i) {
      if (i == 3) {
        int t = 0;
      }
      dfs(i);
    }
    sort(Q + 1, Q + q + 1, cmp);
    string ans(q, '0');
    int pos = m + 1;
    int mmin = 1e7;
    for (int i = 1; i <= q; ++i) {
      int l = Q[i].first.first;
      int r = Q[i].first.second;
      int Index = Q[i].second;
      while (pos > l) {
        pos--;
        mmin = min(mmin, E[pos]);
      }
      if (r >= mmin) {
        ans[Index] = '1';
      }
    }
    cout << ans << endl;
  }
  return 0;
}
