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;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
const ll llinf = (1ll << 61) - 1;
const double eps = 1e-6, ldeps = 1e-9;
struct Dbg {
  static constexpr auto &os = cout;
  template <class C>
  static auto dud(C *x) -> decltype(os << *x, 0);
  template <class C>
  static char dud(...);
  template <class C>
  typename enable_if<sizeof dud<C>(0) != 1, Dbg &>::type operator<<(
      const C &x) {
    os << x;
    return *this;
  }
  template <class C>
  Dbg &dump(C b, C e) {
    *this << "\n[";
    int cur = 0;
    for (C i = b; i != e and cur < 26; i++, cur++)
      *this << ", " + 2 * (i == b) << *i;
    return *this << ']';
  }
  template <class C>
  typename enable_if<sizeof dud<C>(0) == 1, Dbg &>::type operator<<(
      const C &x) {
    return dump(begin(x), end(x));
  }
  template <class C, size_t X>
  typename enable_if<!is_same<C, const char>::value, Dbg &>::type operator<<(
      C (&x)[X]) {
    return dump(begin(x), end(x));
  }
  template <class B, class C>
  Dbg &operator<<(const pair<B, C> &x) {
    return *this << '{' << x.first << ", " << x.second << '}';
  }
  template <class C, size_t Y>
  struct TP {
    void operator()(Dbg &os, const C &t) {
      TP<C, Y - 1>()(os, t);
      os << ", " << get<Y - 1>(t);
    }
  };
  template <class C>
  struct TP<C, 1> {
    void operator()(Dbg &os, const C &t) { os << get<0>(t); }
  };
  template <class... C>
  Dbg &operator<<(const tuple<C...> &t) {
    os << '{', TP<decltype(t), sizeof...(C)>()(*this, t);
    return *this << '}';
  }
  Dbg &operator<<(ostream &(*x)(std::ostream &)) {
    os << x;
    return *this;
  }
} dbg;
void err(istringstream *iss) { delete iss; }
template <class C, class... Args>
void err(istringstream *iss, const C &val, const Args &...args) {
  string name;
  *iss >> name;
  if (name.back() == ',') name.pop_back();
  dbg << name << " = " << val << "; ", err(iss, args...);
}
int T, Q, cn;
const int inf = 1000000007, mxn = 200005, rootn = 440;
int n, m, p[mxn], revp[mxn], a[mxn], prv[mxn], nxt[mxn], root[mxn], mn[mxn];
vector<int> pos[mxn];
template <class T, int N, class cmp = less<T>>
class SparseTable {
  int lookup[22][N + 2], log_2[N + 2];

 public:
  T ara[N + 2];
  SparseTable() {
    log_2[1] = 0;
    for (int i = 2; i < N; i++) log_2[i] = log_2[i >> 1] + 1;
  }
  void preprocess(int nd) {
    for (int i = 0; i <= nd; i++) lookup[0][i] = i;
    for (int j = 1; (1 << j) <= nd + 1; j++) {
      for (int i = 0; (i + (1 << j) - 1) <= nd; i++) {
        lookup[j][i] =
            cmp()(ara[lookup[j - 1][i]], ara[lookup[j - 1][i + (1 << (j - 1))]])
                ? lookup[j - 1][i]
                : lookup[j - 1][i + (1 << (j - 1))];
      }
    }
  }
  int query(int L, int R) {
    int j = log_2[R - L + 1];
    return cmp()(ara[lookup[j][L]], ara[lookup[j][R - (1 << j) + 1]])
               ? ara[lookup[j][L]]
               : ara[lookup[j][R - (1 << j) + 1]];
  }
};
SparseTable<int, mxn> st;
int go(int pos, int trgt) {
  if (!trgt) return pos;
  while (pos <= m and a[pos] + rootn <= trgt) pos = root[pos];
  while (pos <= m and a[pos] != trgt) pos = nxt[pos];
  return pos;
}
signed main() {
  ios::sync_with_stdio(0);
  cin.tie(NULL);
  cout.precision(11);
  cin >> n >> m >> Q;
  for (int i = 1; i <= n; i++) {
    cin >> p[i], revp[p[i]] = i;
  }
  for (int i = 1; i <= m; i++) {
    cin >> a[i], a[i] = revp[a[i]];
    pos[a[i]].push_back(i);
  }
  for (int i = 1; i <= m; i++) {
    int trgt = a[i] == n ? 1 : a[i] + 1;
    auto itp = lower_bound(begin(pos[a[i] - 1]), end(pos[a[i] - 1]), i),
         itn = lower_bound(begin(pos[trgt]), end(pos[trgt]), i);
    prv[i] = itp == pos[a[i] - 1].begin() ? 0 : *--itp,
    nxt[i] = itn == pos[trgt].end() ? m + 1 : *itn;
  }
  prv[m + 1] = nxt[m + 1] = root[m + 1] = m + 1;
  for (int i = m; i >= 1; i--) {
    if (a[i] + rootn > n)
      root[i] = m + 1;
    else {
      int tmp = i;
      for (int j = 0; j < rootn; j++) {
        tmp = nxt[tmp];
      }
      root[i] = tmp;
    }
  }
  for (int i = 1; i <= m; i++) {
    mn[i] = a[i] > 1 ? go(nxt[go(i, n)], a[i] - 1) : go(i, n);
    st.ara[i] = mn[i];
  }
  st.preprocess(m);
  for (int i = 0; i < Q; i++) {
    int l, r;
    cin >> l >> r;
    cout << (st.query(l, r) <= r);
  }
  cout << '\n';
}
