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 T>
void print(vector<T> s) {
  for (T i : s) cout << i << " ";
  cout << endl;
}
struct SegmentTreeMax {
  int b;
  vector<int> tree;
  static const int inf = 1e9 + 7;
  SegmentTreeMax(int n) {
    b = 0;
    while ((1 << b) < n) b++;
    b = (1 << b);
    tree.resize(2 * b);
    fill(tree.begin(), tree.end(), -inf);
  }
  inline void update(int pos, int value) {
    pos += b;
    tree[pos] = value;
    while (pos > 0) {
      pos >>= 1;
      tree[pos] = max(tree[pos << 1], tree[(pos << 1) | 1]);
    }
  }
  long long getMax(int v, int vl, int vr, int l, int r) {
    if (vl >= r || vr <= l) return -inf;
    if (vl >= l && vr <= r) return tree[v];
    int vm = (vl + vr) >> 1;
    return max(getMax(v << 1, vl, vm, l, r),
               getMax((v << 1) | 1, vm, vr, l, r));
  }
  long long get(int l, int r) { return getMax(1, 0, b, l, r); }
};
const int maxn = 2e5 + 7;
int p[maxn], asasdka[maxn];
int s[maxn];
int last[maxn];
const int kek = 19;
int go[kek][maxn];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n, m, q;
  cin >> n >> m >> q;
  for (int i = 0; i < n; i++) {
    cin >> p[i];
    p[i]--;
    asasdka[p[i]] = i;
  }
  fill(last, last + n, -1);
  for (int j = 0; j < m; j++) {
    cin >> s[j];
    s[j]--;
    int prev = asasdka[s[j]] - 1;
    if (prev == -1) prev = n - 1;
    go[0][j] = last[p[prev]];
    last[s[j]] = j;
  }
  for (int i = 1; i < kek; i++) {
    for (int j = 0; j < m; j++) {
      if (go[i - 1][j] != -1)
        go[i][j] = go[i - 1][go[i - 1][j]];
      else
        go[i][j] = -1;
    }
  }
  SegmentTreeMax tree = SegmentTreeMax(m);
  for (int i = 0; i < m; i++) {
    int cur = n - 1, now = i;
    for (int j = kek - 1; j >= 0; j--) {
      if (cur >= (1 << j)) {
        if (now != -1) now = go[j][now];
        cur -= (1 << j);
      }
    }
    tree.update(i, now);
  }
  while (q-- > 0) {
    int l, r;
    cin >> l >> r;
    if (tree.get(l - 1, r) >= l - 1)
      cout << 1;
    else
      cout << 0;
  }
  cout << endl;
  return 0;
}
