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 n, m, Q, p[200003], a[200003], b[200003], pos[200003], fa[200003][23],
    dep[200003], pre[200003], t[200003 << 2];
void build(int p, int l, int r) {
  if (l == r) {
    t[p] = pre[l];
    return;
  }
  int mid = (l + r) >> 1;
  build(p << 1, l, mid);
  build(p << 1 | 1, mid + 1, r);
  t[p] = max(t[p << 1], t[p << 1 | 1]);
}
int query(int p, int l, int r, int seg_l, int seg_r) {
  if (seg_l <= l && r <= seg_r) return t[p];
  int mid = (l + r) >> 1, ret = 0;
  if (seg_l <= mid) ret = max(ret, query(p << 1, l, mid, seg_l, seg_r));
  if (seg_r > mid) ret = max(ret, query(p << 1 | 1, mid + 1, r, seg_l, seg_r));
  return ret;
}
int main() {
  scanf("%d%d%d", &n, &m, &Q);
  for (int i = 1; i < n; i++) scanf("%d", p + i), pos[p[i]] = i;
  scanf("%d", p), pos[p[0]] = 0;
  for (int i = 1; i <= m; i++) scanf("%d", a + i);
  dep[0] = -1;
  for (int u = 1; u <= m; u++) {
    int last = b[p[(pos[a[u]] + n - 1) % n]];
    fa[u][0] = last;
    dep[u] = dep[last] + 1;
    for (int i = 1; (1 << i) <= dep[u]; i++) fa[u][i] = fa[fa[u][i - 1]][i - 1];
    b[a[u]] = u;
    int x = u;
    for (int i = 0; (1 << i) <= n - 1; i++)
      if (((n - 1) >> i) & 1) x = fa[x][i];
    pre[u] = x;
  }
  build(1, 1, m);
  while (Q--) {
    int l, r;
    scanf("%d%d", &l, &r);
    putchar((query(1, 1, m, l, r) >= l) + '0');
  }
  return 0;
}
