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;
int kolejnosc[200005], premutacja[200005], ciag[200005], najblizszy[200005],
    drzewo[530000];
int pointer_jump[200005][20], potegi[20];
int rozmiar = 1, pomoc;
void buduj() {
  pomoc /= 2;
  for (int i = pomoc; i < pomoc * 2; i++)
    drzewo[i] = min(drzewo[i * 2], drzewo[i * 2 + 1]);
  if (pomoc > 1) buduj();
}
int znajdz(int p, int k, int a, int b, int x) {
  if (p > b || k < a) return 1000000000;
  if (a >= p && k >= b) return drzewo[x];
  int min_l = znajdz(p, k, a, (a + b) / 2, x * 2);
  int min_p = znajdz(p, k, (a + b) / 2 + 1, b, x * 2 + 1);
  return min(min_l, min_p);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int dlugpsc_permutacji, dlugpsc_ciagu, liczba_zapytan;
  cin >> dlugpsc_permutacji >> dlugpsc_ciagu >> liczba_zapytan;
  for (int i = 1; i <= dlugpsc_permutacji; i++) {
    cin >> premutacja[i];
    if (i != 1) kolejnosc[premutacja[i - 1]] = premutacja[i];
  }
  kolejnosc[premutacja[dlugpsc_permutacji]] = premutacja[1];
  for (int i = 1; i <= dlugpsc_ciagu; i++) cin >> ciag[i];
  for (int i = 1; i <= dlugpsc_permutacji; i++) najblizszy[i] = 1000000000;
  for (int i = dlugpsc_ciagu; i > 0; i--) {
    najblizszy[ciag[i]] = i;
    pointer_jump[i][0] = najblizszy[kolejnosc[ciag[i]]];
  }
  potegi[0] = 1;
  for (int i = 1; i < 20; i++) potegi[i] = potegi[i - 1] * 2;
  int potega = 0;
  int pomocnicza = dlugpsc_ciagu;
  while (pomocnicza > 0) {
    pomocnicza /= 2;
    potega++;
  }
  for (int j = 1; j <= potega; j++) {
    for (int i = 1; i <= dlugpsc_ciagu; i++) {
      if (pointer_jump[i][j - 1] < 1000000000) {
        pointer_jump[i][j] = pointer_jump[pointer_jump[i][j - 1]][j - 1];
      } else
        pointer_jump[i][j] = 1000000000;
    }
  }
  for (int i = potegi[potega]; i < potegi[potega] * 2; i++)
    drzewo[i] = 1000000000;
  for (int i = potegi[potega]; i < potegi[potega] + dlugpsc_ciagu; i++) {
    pomocnicza = dlugpsc_permutacji - 1;
    int indeks = i - potegi[potega] + 1, xd = potega;
    while (pomocnicza > 0) {
      while (potegi[xd] > pomocnicza) xd--;
      pomocnicza -= potegi[xd];
      indeks = pointer_jump[indeks][xd];
      if (indeks == 1000000000) break;
    }
    drzewo[i] = indeks;
  }
  while (rozmiar <= dlugpsc_ciagu) rozmiar *= 2;
  pomoc = rozmiar;
  buduj();
  int a, b;
  for (int i = 0; i < liczba_zapytan; i++) {
    cin >> a >> b;
    pomoc = znajdz(a - 1, b - 1, 0, rozmiar - 1, 1);
    if (pomoc <= b)
      cout << 1;
    else
      cout << 0;
  }
}
