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 INF = 1e9;
const int NMAX = 2e5 + 5;
const int LOGM = 18;
int N, M, Q;
int where[NMAX + 2];
int p[2 * NMAX + 2], v[NMAX + 2], go[LOGM + 1][NMAX + 2];
int need[NMAX + 2], rmq[LOGM + 1][NMAX + 2];
int Log2[NMAX + 2];
int last_encounter[NMAX + 2];
int main() {
  Log2[0] = -1;
  for (int i = 1; i <= NMAX; ++i) Log2[i] = Log2[i / 2] + 1;
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> N >> M >> Q;
  for (int i = 1; i <= N; ++i) {
    cin >> p[i];
    p[N + i] = p[i];
    where[p[i]] = i;
  }
  for (int i = 1; i <= M; ++i) cin >> v[i];
  for (int i = M; i >= 1; --i) {
    int next_val = p[where[v[i]] + 1];
    go[0][i] = last_encounter[next_val];
    for (int j = 1; j <= LOGM; ++j) go[j][i] = go[j - 1][go[j - 1][i]];
    last_encounter[v[i]] = i;
  }
  for (int i = M; i >= 1; --i) {
    int pos = i, rem = N - 1, step = LOGM;
    while (pos && step >= 0) {
      if (rem >= (1 << step)) pos = go[step][pos], rem -= (1 << step);
      step--;
    }
    need[i] = (pos != 0 ? pos : INF);
    rmq[0][i] = need[i];
    for (int j = 1; j <= LOGM; ++j) {
      rmq[j][i] = rmq[j - 1][i];
      if (i + (1 << j) / 2 <= M)
        rmq[j][i] = min(rmq[j][i], rmq[j - 1][i + (1 << j) / 2]);
    }
  }
  for (int i = 1; i <= Q; ++i) {
    int st, dr;
    cin >> st >> dr;
    int lg = dr - st + 1;
    int p = Log2[lg];
    int r = min(rmq[p][st], rmq[p][dr - (1 << p) + 1]);
    if (r <= dr)
      cout << '1';
    else
      cout << '0';
  }
  cout << '\n';
  return 0;
}
