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;
mt19937 gen(chrono::system_clock::now().time_since_epoch().count());
const int N = 2e5 + 10;
const long long MOD = 1e9 + 7;
const int rx[4] = {-1, 0, 1, 0};
const int ry[4] = {0, 1, 0, -1};
const long double eps = 1e-7;
const long double pi = acos(-1.0);
const int INF = 2e9;
vector<int> g[N];
vector<int> e;
bool used[N];
int d[N], l[N], n;
void dfs(int v, int deep) {
  d[v] = deep;
  used[v] = true;
  e.push_back(v);
  if (deep + 1 >= n) {
    l[v] = e[deep + 1 - n];
  } else
    l[v] = -INF;
  for (auto to : g[v]) {
    if (!used[to]) dfs(to, deep + 1);
  }
  e.pop_back();
}
struct segtree {
  vector<int> t;
  int nw;
  segtree(int n) {
    nw = (1 << (32 - __builtin_clz(n) - (__builtin_popcount(n) == 1)));
    t.resize(nw << 1, -INF);
  }
  void modify(int v, int cl, int cr, int pos, int val) {
    if (cr - cl == 1) {
      t[v] = val;
      return;
    }
    int mid = (cl + cr) / 2;
    if (pos < mid)
      modify(v * 2, cl, mid, pos, val);
    else
      modify(v * 2 + 1, mid, cr, pos, val);
    t[v] = max(t[v * 2], t[v * 2 + 1]);
  }
  void modify(int pos, int val) { modify(1, 1, nw + 1, pos + 1, val + 1); }
  int mn(int v, int cl, int cr, int l, int r) {
    if (cl >= l && cr <= r) {
      return t[v];
    }
    if (cl >= r || cr <= l) return -INF;
    int mid = (cl + cr) / 2;
    return max(mn(v * 2, cl, mid, l, r), mn(v * 2 + 1, mid, cr, l, r));
  }
  int mn(int l, int r) { return mn(1, 1, nw + 1, l, r + 1); }
};
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int m, q;
  cin >> n >> m >> q;
  int p[n];
  for (int i = 0; i < n; i++) cin >> p[i];
  int b[m];
  for (int i = 0; i < m; i++) cin >> b[i];
  int pr[n + 1];
  vector<int> pos(n + 1, -1);
  pr[p[0]] = p[n - 1];
  for (int i = 1; i < n; i++) {
    pr[p[i]] = p[i - 1];
  }
  for (int i = 0; i < m; i++) {
    if (pos[pr[b[i]]] == -1) {
      pos[b[i]] = i;
      continue;
    }
    g[pos[pr[b[i]]]].push_back(i);
    g[i].push_back(pos[pr[b[i]]]);
    pos[b[i]] = i;
  }
  segtree ts(m);
  for (int i = 0; i < m; i++) {
    if (!used[i]) {
      dfs(i, 0);
    }
    ts.modify(i, l[i]);
  }
  for (int i = 0; i < q; i++) {
    int l, r;
    cin >> l >> r;
    int x = ts.mn(l, r);
    if (x >= l && x <= r)
      cout << "1";
    else
      cout << "0";
  }
  return 0;
}
