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 my>
my aabs(const my &a) {
  return (a > 0) ? a : -a;
}
long long int gcd(long long int a, long long int b) {
  return (b == 0) ? a : gcd(b, a % b);
}
long long int LSOne(long long int k) { return (k & (-k)); }
inline int inv(int o) {
  int b = 1000000007, u = 0, v = 1, t, a = o;
  while (a) {
    t = b / a;
    b -= t * a;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  if (u < 0) u += 1000000007;
  return u;
}
inline int add(const int &a, const int &b) {
  return a + b >= 1000000007 ? a + b - 1000000007 : a + b;
}
inline int sub(const int &a, const int &b) {
  return a - b < 0 ? a - b + 1000000007 : a - b;
}
inline int mul(const int &a, const int &b) {
  return int(a * 1ll * b % 1000000007);
}
inline int _div(const int &a, const int &b) { return mul(a, inv(b)); }
inline int pow(int a, int b) {
  int ans = 1;
  while (b) {
    if (b & 1) ans = mul(ans, a);
    a = mul(a, a);
    b >>= 1;
  }
  return ans;
}
void cord(int arr[], int n) {
  int ind = 0;
  map<int, int> mp;
  vector<int> brr(arr, arr + n);
  sort(brr.begin(), brr.end());
  brr.erase(unique(brr.begin(), brr.end()), brr.end());
  for (int i = 0; i < brr.size(); i++) mp[brr[i]] = ind++;
  for (int i = 0; i < n; i++) arr[i] = mp[arr[i]];
}
int par[200010][20], arr[200005], pos[200005], brr[200005], value[2000005];
void com(int diff, int m) {
  for (int i = 1; i < m + 1; i++) {
    arr[i] = i;
    for (int j = 0; j < 20; j++)
      if ((diff >> j) & 1) arr[i] = par[arr[i]][j];
  }
}
void solve() {
  int n, m, q, u, v;
  cin >> n >> m >> q;
  for (int i = 1; i < n + 1; i++) {
    cin >> arr[i];
    pos[arr[i]] = i;
  }
  arr[n + 1] = arr[1];
  for (int i = 0; i < n + 2; i++) value[i] = m + 1;
  for (int i = 1; i < m + 1; i++) cin >> brr[i];
  par[m + 1][0] = m + 1;
  par[0][0] = m + 1;
  for (int i = m; i > 0; i--) {
    par[i][0] = value[arr[pos[brr[i]] + 1]];
    value[brr[i]] = i;
  }
  for (int j = 1; j < 20; j++)
    for (int i = 1; i < m + 2; i++) par[i][j] = par[par[i][j - 1]][j - 1];
  com(n - 1, m);
  for (int i = m - 1; i > 0; i--) arr[i] = min(arr[i + 1], arr[i]);
  while (q--) {
    cin >> u >> v;
    if (v >= arr[u])
      cout << 1;
    else
      cout << 0;
  }
  cout << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
  int t = 1;
  while (t--) solve();
}
