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;
struct query {
  int l, r, id;
  friend bool operator<(query a, query b) { return a.r < b.r; }
} q[200020];
int n, m, qnum, a[200020], b[200020], dya[200020], dyb[200020], len[200020],
    st[200020], mxl;
int ans[200020];
int sum[10000000], lson[10000000], rson[10000000], rt[200020], tot;
void add(int &now, int pre, int l, int r, int p, int w) {
  now = ++tot;
  sum[now] = sum[pre] + w;
  if (l == r) return;
  if (p <= (l + r >> 1))
    add(lson[now], lson[pre], l, l + r >> 1, p, w), rson[now] = rson[pre];
  else
    add(rson[now], rson[pre], (l + r >> 1) + 1, r, p, w), lson[now] = lson[pre];
}
int qmin(int k, int l, int r) {
  if (l == r) return l;
  if (sum[lson[k]])
    return qmin(lson[k], l, l + r >> 1);
  else
    return qmin(rson[k], (l + r >> 1) + 1, r);
}
int main() {
  scanf("%d %d %d", &n, &m, &qnum);
  for (int i = 1; i <= n; ++i) scanf("%d", &a[i]), dya[a[i]] = i;
  a[0] = a[n];
  for (int i = 1; i <= m; ++i) {
    scanf("%d", &b[i]), dyb[b[i]] = i;
    int last = dyb[a[dya[b[i]] - 1]];
    add(rt[i], rt[last], 1, m, i, 1);
    if (len[last] == n) add(rt[i], rt[i], 1, m, qmin(rt[last], 1, m), -1);
    st[i] = qmin(rt[i], 1, m);
    len[i] = min(len[last] + 1, n);
  }
  int x, y;
  for (int i = 1; i <= qnum; ++i) {
    scanf("%d %d", &q[i].l, &q[i].r);
    q[i].id = i;
  }
  sort(q + 1, q + 1 + qnum);
  int last = 1;
  for (int i = 1; i <= qnum; ++i) {
    while (last <= q[i].r) {
      if (len[last] == n) mxl = max(mxl, st[last]);
      ++last;
    }
    ans[q[i].id] = mxl >= q[i].l;
  }
  for (int i = 1; i <= qnum; ++i) printf("%d", ans[i]);
  return 0;
}
