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 int N = 2e5 + 10;
const int mod = 998244353;
const int inf = 0x3f3f3f3f;
int p[N], pre[N];
int a[N], lg[N];
int f[N][27];
int g[N][27];
int lst[N];
void init() {
  lg[1] = 0;
  lg[2] = 1;
  for (int i = 3; i <= 200000; i++) {
    lg[i] = lg[i >> 1] + 1;
  }
}
int get(int l, int r) {
  int k = lg[r - l + 1];
  return max(g[l][k], g[r - (1 << k) + 1][k]);
}
int main() {
  ios::sync_with_stdio(false);
  int n, m, q;
  cin >> n >> m >> q;
  int i;
  init();
  for (i = 1; i <= n; i++) {
    cin >> p[i];
  }
  for (i = 1; i <= m; i++) {
    cin >> a[i];
  }
  p[0] = p[n];
  for (i = 1; i <= n; i++) {
    pre[p[i]] = p[i - 1];
  }
  for (i = 1; i <= m; i++) {
    f[i][0] = lst[pre[a[i]]];
    lst[a[i]] = i;
  }
  for (i = 1; i <= 25; i++) {
    for (int j = 1; j <= m; j++) {
      f[j][i] = f[f[j][i - 1]][i - 1];
    }
  }
  for (i = 1; i <= m; i++) {
    g[i][0] = i;
    for (int j = 0; j <= lg[n - 1]; j++) {
      if ((n - 1) & (1 << j)) {
        g[i][0] = f[g[i][0]][j];
      }
    }
  }
  for (i = 1; i <= lg[m]; i++) {
    for (int j = 1; j + (1 << i) - 1 <= m; j++) {
      g[j][i] = max(g[j][i - 1], g[j + (1 << i - 1)][i - 1]);
    }
  }
  string s = "";
  while (q--) {
    int l, r;
    cin >> l >> r;
    if (get(l, r) >= l) {
      s += '1';
    } else {
      s += '0';
    }
  }
  cout << s << endl;
}
