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;
using ld = long double;
const ll INFll = 1ll * 1000000007 * 1000000007;
const long double PI =
    3.141592653589793238462643383279502884197169399375105820974944;
ll gcd(ll a, ll b) { return (b == 0) ? a : gcd(b, a % b); }
int min(int a, int b) { return ((a > b) ? b : a); }
const int N = 2 * 1e5 + 5;
int n, m, q;
int per[N], nxt[N], ar[N];
vector<vector<int>> jump(N, vector<int>(20));
map<int, int> fn, cp;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> n >> m >> q;
  for (ll i = 0; i <= n - 1; i++) cin >> per[i];
  for (ll i = 1; i <= m; i++) cin >> ar[i];
  for (ll i = 0; i <= n - 1; i++) nxt[per[i]] = per[(i + 1) % n];
  for (ll i = 1; i <= n; i++) fn[i] = m + 1;
  for (ll i = m; i >= 1; i--) {
    jump[i][0] = fn[nxt[ar[i]]];
    fn[ar[i]] = i;
  }
  jump[m + 1][0] = m + 1;
  for (ll i = 1; i <= 18; i++) {
    for (ll j = 1; j <= m + 1; j++) {
      jump[j][i] = jump[jump[j][i - 1]][i - 1];
    }
  }
  n--;
  int mi = m + 1;
  for (ll i = m; i >= 1; i--) {
    int pos = i;
    for (ll j = 18; j >= 0; j--) {
      if (1 << j & n) pos = jump[pos][j];
    }
    if (pos <= m) mi = min(mi, pos);
    cp[i] = mi;
  }
  int a, b;
  for (ll i = 1; i <= q; i++) {
    cin >> a >> b;
    if (cp[a] <= b)
      cout << 1;
    else
      cout << 0;
  }
  cout << '\n';
}
