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;
int nw;
int tree[5000000], lefto[5000000], righto[5000000];
int tree2[1500000];
int ara[300000], preve[300000], root[300000];
int update(int node, int st, int en, int l) {
  if (st > l or en < l) return node;
  int ps = ++nw;
  if (st == en) {
    tree[ps] = 1;
    return ps;
  }
  int mid = (st + en) >> 1;
  lefto[ps] = update(lefto[node], st, mid, l);
  righto[ps] = update(righto[node], mid + 1, en, l);
  tree[ps] = tree[righto[ps]] + tree[lefto[ps]];
  return ps;
}
int sum, ck;
void query(int node, int st, int en) {
  if (tree[node] < sum) {
    sum -= tree[node];
    return;
  }
  if (st == en) {
    ck = st;
    sum = 0;
    return;
  }
  int mid = (st + en) >> 1;
  query(righto[node], mid + 1, en);
  if (ck) return;
  query(lefto[node], st, mid);
}
void update2(int node, int st, int en, int pos, int v) {
  if (st > pos or en < pos) return;
  if (st == en) {
    tree2[node] = v;
    return;
  }
  int mid = (st + en) >> 1;
  update2(node * 2, st, mid, pos, v);
  update2(node * 2 + 1, mid + 1, en, pos, v);
  tree2[node] = max(tree2[node * 2], tree2[node * 2 + 1]);
}
int query2(int node, int st, int en, int l, int r) {
  if (st > r or en < l) return 0;
  if (st >= l and en <= r) return tree2[node];
  int mid = (st + en) >> 1;
  int f = query2(node * 2, st, mid, l, r);
  int g = query2(node * 2 + 1, mid + 1, en, l, r);
  return max(f, g);
}
int main() {
  int i, j, k, l, m, n, q;
  scanf("%d%d%d", &n, &m, &q);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &ara[i]);
    preve[ara[i]] = ara[i - 1];
  }
  preve[ara[1]] = ara[n];
  for (int i = 1; i <= m; i++) {
    scanf("%d", &l);
    int c = preve[l];
    root[l] = update(root[c], 1, m, i);
    if (tree[root[l]] < n) continue;
    ck = 0;
    sum = n;
    query(root[l], 1, m);
    update2(1, 1, m, i, ck);
  }
  string str;
  for (int i = 1; i <= q; i++) {
    scanf("%d%d", &l, &k);
    int ans = query2(1, 1, m, l, k);
    if (ans >= l)
      str += "1";
    else
      str += "0";
  }
  cout << str << endl;
}
