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;
const long long MOD = (1e9 + 7);
const long long INF = (1e9 + 123456789);
const long long INFL = (INF * INF);
inline long long addm(long long a, long long b, long long m = MOD) {
  return ((a + b) % m);
}
inline long long subm(long long a, long long b, long long m = MOD) {
  return (((a - b) % m + m) % m);
}
inline long long mulm(long long a, long long b, long long m = MOD) {
  return ((a * b) % m);
}
long long powm(long long a, long long b, long long m = MOD) {
  long long ret = (!b) ? 1 : powm(a, b / 2);
  return (!b) ? 1 : mulm(mulm(ret, ret, m), b % 2 ? a : 1, m);
}
long long gcd(long long a, long long b) { return (!b) ? a : gcd(b, a % b); }
long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
long long inv(long long x, long long m = MOD) { return powm(x, m - 2, m); }
int p[200500], s[200500];
int l[200500], pr[200500], prv[200500][20], h[200500][20];
void solve() {
  memset(pr, -1, sizeof(pr));
  memset(prv, -1, sizeof(prv));
  memset(l, -1, sizeof(l));
  int n, m, q;
  cin >> n >> m >> q;
  for (int i = 0; i < n; i++) cin >> p[i];
  for (int i = 0; i < n; i++) pr[p[(i + 1) % n]] = p[i];
  for (int i = 0; i < m; i++) cin >> s[i];
  for (int i = 0; i < m; i++) {
    prv[i][0] = (pr[s[i]] == -1) ? -1 : l[pr[s[i]]];
    l[s[i]] = i;
  }
  for (int i = 1; i < 20; i++) {
    for (int j = 0; j < m; j++) {
      if (prv[j][i - 1] == -1)
        prv[j][i] = -1;
      else
        prv[j][i] = prv[prv[j][i - 1]][i - 1];
    }
  }
  for (int i = 0; i < m; i++) {
    int d = n - 1;
    int v = i;
    for (int j = 20 - 1; v != -1 && j >= 0; j--) {
      if (d >= (1 << j)) {
        d -= (1 << j);
        v = prv[v][j];
      }
    }
    h[i][0] = v;
  }
  for (int l = 1; l < 20; l++) {
    int d = (1 << l);
    for (int i = 0; i + d - 1 < m; i++) {
      h[i][l] = max(h[i][l - 1], h[i + (d >> 1)][l - 1]);
      ;
      ;
      ;
    }
  }
  string ans;
  while (q--) {
    int l, r;
    cin >> l >> r;
    --l;
    --r;
    int d = (r - l + 1);
    int lg = 0;
    while (d >= (1 << lg)) lg++;
    lg--;
    int mx = max(h[l][lg], h[r - (1 << lg) + 1][lg]);
    if (mx >= l)
      ans.push_back('1');
    else
      ans.push_back('0');
  }
  cout << ans << "\n";
}
int main(int argc, char *argv[]) {
  cin.sync_with_stdio(0);
  cin.tie(NULL);
  solve();
  return 0;
}
