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 LOGNMAX = 30;
const int NMAX = 2e5 + 7;
const int INF = 2e6 + 7;
int n, m, Q;
int p[NMAX], a[NMAX];
int vidjen[NMAX];
int skoci[LOGNMAX][NMAX];
int sled[NMAX];
int treba[NMAX];
struct segTree {
  int t[4 * NMAX];
  void update(int node, int st, int en, int idx, int val) {
    if (st == en) {
      t[node] = val;
      return;
    }
    int mid = (st + en) / 2;
    if (idx <= mid)
      update(2 * node, st, mid, idx, val);
    else
      update(2 * node + 1, mid + 1, en, idx, val);
    t[node] = min(t[2 * node], t[2 * node + 1]);
  }
  int get(int node, int st, int en, int l, int r) {
    if (r < st || l > en || st > en) return INF;
    if (l <= st && en <= r) return t[node];
    int mid = (st + en) / 2;
    int m1 = get(2 * node, st, mid, l, r);
    int m2 = get(2 * node + 1, mid + 1, en, l, r);
    return min(m1, m2);
  }
} T;
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n >> m >> Q;
  for (int i = 1; i <= n; i++) cin >> p[i];
  for (int i = 1; i <= m; i++) cin >> a[i];
  for (int i = 1; i <= n - 1; i++) sled[p[i]] = p[i + 1];
  sled[p[n]] = p[1];
  for (int i = 1; i <= n; i++) vidjen[i] = m + 1;
  skoci[0][m + 1] = m + 1;
  for (int i = m; i; i--) {
    skoci[0][i] = vidjen[sled[a[i]]];
    vidjen[a[i]] = i;
  }
  for (int i = 1; i < LOGNMAX; i++)
    for (int j = 1; j <= m + 1; j++)
      skoci[i][j] = skoci[i - 1][skoci[i - 1][j]];
  for (int i = 1; i <= m; i++) {
    int idi = i;
    for (int j = 0; j < 22; j++)
      if ((n - 1) & (1 << j)) idi = skoci[j][idi];
    treba[i] = idi;
  }
  for (int i = 1; i <= m; i++) T.update(1, 1, m, i, treba[i]);
  while (Q--) {
    int l, r;
    cin >> l >> r;
    int odg = T.get(1, 1, m, l, r) <= r;
    cout << odg;
  }
  return 0;
}
