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;
template <class T>
struct RMQ {
  vector<vector<T>> st;
  vector<int> log;
  T combine(T a, T b) { return min(a, b); }
  void init(vector<T> a) {
    int n = a.size();
    log = vector<int>(n + 1);
    for (int i = 2; i <= n; ++i) log[i] = log[i >> 1] + 1;
    int k = log[n];
    st = vector<vector<T>>(n, vector<T>(k + 1));
    for (int i = 0; i < n; ++i) st[i][0] = a[i];
    for (int j = 1; j <= k; ++j)
      for (int i = 0; i + (1 << j) - 1 < n; ++i)
        st[i][j] = combine(st[i][j - 1], st[i + (1 << (j - 1))][j - 1]);
  }
  T qry(int l, int r) {
    int k = log[r - l + 1];
    return combine(st[l][k], st[r - (1 << k) + 1][k]);
  }
};
const int mxN = 200000;
int n, m, q, p[mxN], a[mxN], nxt[mxN], oc[mxN], dp[mxN][18];
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> m >> q;
  for (int i = 0; i < n; ++i) cin >> p[i], --p[i];
  for (int i = 0; i < m; ++i) cin >> a[i], --a[i];
  for (int i = 0; i < n; ++i) nxt[p[i]] = p[(i + 1) % n];
  memset(oc, -1, sizeof(oc));
  for (int i = m - 1; ~i; --i) {
    dp[i][0] = oc[nxt[a[i]]];
    for (int j = 1; j < 18; ++j)
      dp[i][j] = dp[i][j - 1] ^ -1 ? dp[dp[i][j - 1]][j - 1] : -1;
    oc[a[i]] = i;
  }
  vector<int> v(m);
  for (int i = 0; i < m; ++i) {
    int c = i;
    for (int j = 17; ~j; --j)
      if (n - 1 >> j & 1) c = c ^ -1 ? dp[c][j] : -1;
    v[i] = c ^ -1 ? c : 69696969;
  }
  RMQ<int> rmq;
  rmq.init(v);
  while (q--) {
    int l, r;
    cin >> l >> r, --l, --r;
    cout << (rmq.qry(l, r) <= r);
  }
  return 0;
}
