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;
template <class c>
struct rge {
  c b, e;
};
template <class c>
rge<c> range(c i, c j) {
  return rge<c>{i, j};
}
template <class c>
auto dud(c* x) -> decltype(cerr << *x, 0);
template <class c>
char dud(...);
struct debug {
  template <class c>
  debug& operator<<(const c&) {
    return *this;
  }
};
using ll = long long;
const int nax = 2e5 + 5;
int inv[nax];
int a[nax];
int nxt[nax];
int up_to[nax];
int down_to[nax];
vector<int> queries[nax];
vector<int> process[nax];
int best[nax];
int answer[nax];
int must[nax];
int main() {
  int n, m, q;
  scanf("%d%d%d", &n, &m, &q);
  for (int i = 1; i <= n; ++i) {
    int x;
    scanf("%d", &x);
    inv[x] = i;
  }
  for (int i = 1; i <= m; ++i) {
    int x;
    scanf("%d", &x);
    a[i] = inv[x];
  }
  for (int i = 1; i <= n; ++i) {
    nxt[i] = m + 1;
  }
  up_to[m + 1] = m + 1;
  for (int i = m; i >= 1; --i) {
    nxt[a[i]] = i;
    if (a[i] == n) {
      up_to[i] = i;
      continue;
    }
    up_to[i] = up_to[nxt[a[i] + 1]];
  }
  for (int i = 1; i <= n; ++i) {
    nxt[i] = 0;
  }
  down_to[0] = 0;
  for (int i = 1; i <= m; ++i) {
    nxt[a[i]] = i;
    if (a[i] == 1) {
      down_to[i] = i;
      continue;
    }
    down_to[i] = down_to[nxt[a[i] - 1]];
  }
  debug() << " ["
          << "range(a + 1, a + m + 1)"
             ": "
          << (range(a + 1, a + m + 1)) << "] ";
  debug() << " ["
          << "range(up_to + 1, up_to + m + 1)"
             ": "
          << (range(up_to + 1, up_to + m + 1)) << "] ";
  debug() << " ["
          << "range(down_to + 1, down_to + m + 1)"
             ": "
          << (range(down_to + 1, down_to + m + 1)) << "] ";
  for (int i = 1; i <= m; ++i) {
    queries[up_to[i] + 1].push_back(i);
  }
  for (int i = 0; i <= n; ++i) {
    best[i] = m + 1;
  }
  for (int i = 0; i <= m; ++i) {
    answer[i] = m + 1;
  }
  for (int i = m; i >= 1; --i) {
    process[down_to[i]].push_back(i);
    for (int j : process[i]) {
      best[a[j]] = min(best[a[j]], j);
    }
    for (int j : queries[i]) {
      answer[j] = best[a[j] - 1];
    }
  }
  debug() << " ["
          << "range(answer + 1, answer + m + 1)"
             ": "
          << (range(answer + 1, answer + m + 1)) << "] ";
  must[m + 1] = m + 1;
  for (int i = m; i >= 1; --i) {
    must[i] = must[i + 1];
    if (a[i] == 1) {
      must[i] = min(must[i], up_to[i]);
    } else {
      must[i] = min(must[i], answer[i]);
    }
  }
  debug() << " ["
          << "range(must + 1, must + m + 1)"
             ": "
          << (range(must + 1, must + m + 1)) << "] ";
  while (q--) {
    int L, R;
    scanf("%d%d", &L, &R);
    printf(must[L] <= R ? "1" : "0");
  }
  puts("");
}
