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 maxn = 2e5 + 5;
int n, m, q, a[maxn], b[maxn], pos[maxn];
int nxt[20][maxn], ans[maxn];
vector<pair<int, int> > qu[maxn];
vector<int> adj[maxn];
void readf() {
  scanf("%d%d%d", &n, &m, &q);
  for (int i = (1); i <= (n); ++i) {
    scanf("%d", &a[i]);
    b[a[i]] = i;
  }
  for (int i = (1); i <= (m); ++i) {
    scanf("%d", &a[i]);
    a[i] = b[a[i]];
  }
}
int rgt(int u) {
  int tmp = n;
  for (int k = 18; k >= 0; --k)
    if ((1 << k) < tmp) {
      u = nxt[k][u];
      tmp -= (1 << k);
    }
  return u;
}
void solve() {
  for (int i = m; i > 0; --i) {
    if (pos[a[i] % n + 1]) nxt[0][i] = pos[a[i] % n + 1];
    pos[a[i]] = i;
  }
  for (int k = 1; (1 << k) <= m; ++k)
    for (int i = 1; i + (1 << k) <= m; ++i)
      nxt[k][i] = nxt[k - 1][nxt[k - 1][i]];
  for (int i = 1; i <= m; ++i) adj[rgt(i)].emplace_back(i);
  for (int i = (1); i <= (q); ++i) {
    int l, r;
    scanf("%d%d", &l, &r);
    qu[r].emplace_back(l, i);
  }
  int mx = 0;
  for (int i = 1; i <= m; ++i) {
    for (auto u : adj[i]) mx = max(mx, u);
    for (auto u : qu[i]) ans[u.second] = (mx >= u.first);
  }
  for (int i = 1; i <= q; ++i) printf("%d", ans[i]);
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  readf();
  solve();
}
