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;
int p[200009], a[200009], nxt[200009], r_idx[200009], hop[200009][21],
    hopn[200009], mn[200009][21];
void preprocess() {
  for (int i = m; i >= 1; i--) {
    mn[i][0] = hopn[i];
    for (int j = 1; j < 21; j++) {
      mn[i][j] = mn[i][j - 1];
      int p = i + (1 << (j - 1));
      if (p <= m) {
        mn[i][j] = min(mn[i][j], mn[p][j - 1]);
      }
    }
  }
}
int getmin(int s, int e) {
  int ret = hopn[s];
  int ci = s;
  for (int j = 21 - 1; j >= 0; j--) {
    int ni = ci + (1 << j) - 1;
    if (ni <= e) {
      ret = min(ret, mn[ci][j]);
      ci = ni + 1;
    }
  }
  return ret;
}
int main() {
  cin >> n >> m >> q;
  for (int i = 1; i <= n; i++) scanf("%d", &p[i]);
  for (int i = 1; i <= m; i++) scanf("%d", &a[i]);
  for (int i = 1; i < n; i++) nxt[p[i]] = p[i + 1];
  nxt[p[n]] = p[1];
  int inf = m + 1;
  fill(r_idx, r_idx + n + 2, inf);
  fill(hop[inf], hop[inf] + 21, inf);
  for (int i = m; i >= 1; i--) {
    hop[i][0] = r_idx[nxt[a[i]]];
    for (int j = 1; j < 21; j++) {
      hop[i][j] = hop[hop[i][j - 1]][j - 1];
    }
    r_idx[a[i]] = i;
  }
  for (int i = 1; i <= m; i++) {
    int hops_left = n - 1;
    int dest = i;
    for (int j = 21 - 1; j >= 0; j--) {
      int p = (1 << j);
      if (p <= hops_left) {
        hops_left -= p;
        dest = hop[dest][j];
      }
    }
    hopn[i] = dest;
  }
  preprocess();
  while (q--) {
    int s, e;
    scanf("%d %d", &s, &e);
    if (getmin(s, e) <= e) {
      printf("1");
    } else
      printf("0");
  }
}
