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>
long long mod = 1e9 + 7;
void moduo(long long mod1) { mod = mod1; }
long long powermod(long long a, long long b) {
  long long r = 1;
  while (b) {
    if (b % 2 == 1) {
      r = ((r % mod) * (a % mod)) % mod;
    }
    a = ((a % mod) * (a % mod)) % mod;
    b >>= 1;
  }
  return r;
}
long long inv(long long a) { return powermod(a, mod - 2); }
long long add(long long a, long long b) {
  return (((a % mod) + (b % mod)) % mod + mod) % mod;
}
long long sub(long long a, long long b) {
  return (((a % mod) - (b % mod)) % mod + mod) % mod;
}
long long mul(long long a, long long b) {
  return ((a % mod) * (b % mod)) % mod;
}
long long divide(long long a, long long b) {
  return ((a % mod) * inv(b)) % mod;
}
using namespace std;
const int mn = 2 * 1e5 + 100;
int p[mn];
int a[mn];
int sledeci[mn];
int lift[mn][25];
int kraj[mn];
vector<int> graf;
const int INF = mn + 100;
int spars[mn][25];
int logovi[mn];
int jump(int node, int k) {
  int tr = node;
  int koji = 0;
  while (k > 0) {
    if (k % 2 == 1) tr = lift[tr][koji];
    k /= 2;
    koji++;
  }
  return tr;
}
int main() {
  int n, m, q;
  scanf("%i%i%i", &n, &m, &q);
  for (int i = 0; i < n; i++) scanf("%i", &p[i]);
  for (int i = 0; i < m; i++) scanf("%i", &a[i]);
  for (int i = 0; i < n - 1; i++) sledeci[p[i]] = p[i + 1];
  sledeci[p[n - 1]] = p[0];
  vector<queue<int> > gdesu(n + 1);
  for (int i = 0; i < m; i++) {
    gdesu[a[i]].push(i);
  }
  graf.resize(m);
  for (int i = 0; i < m; i++) {
    int koji = sledeci[a[i]];
    if (!gdesu[koji].empty()) {
      graf[i] = gdesu[koji].front();
    } else {
      graf[i] = i;
    }
    gdesu[a[i]].pop();
  }
  for (int i = 0; i < m; i++) {
    lift[i][0] = graf[i];
  }
  for (int j = 1; j < 25; j++) {
    for (int i = 0; i < m; i++) {
      lift[i][j] = lift[lift[i][j - 1]][j - 1];
    }
  }
  for (int i = 0; i < m; i++) {
    if (sledeci[a[jump(i, n - 1)]] == a[i])
      kraj[i] = jump(i, n - 1);
    else
      kraj[i] = m;
  }
  for (int i = 0; i < m; i++) {
    spars[i][0] = kraj[i];
  }
  for (int j = 1; j < 25; j++) {
    for (int i = 0; i < m; i++) {
      if (i + (1 << (j - 1)) < m)
        spars[i][j] = min(spars[i][j - 1], spars[i + (1 << (j - 1))][j - 1]);
      else
        spars[i][j] = spars[i][j - 1];
    }
  }
  logovi[1] = 0;
  for (int i = 2; i < mn; i++) {
    logovi[i] = logovi[i / 2] + 1;
  }
  string rez = "";
  while (q--) {
    int l, r;
    scanf("%d%d", &l, &r);
    l--;
    r--;
    int kolko = (r - l + 1);
    int gdeje = min(spars[l][logovi[kolko]],
                    spars[r - (1 << logovi[kolko]) + 1][logovi[kolko]]);
    if (gdeje <= r) {
      printf("1");
    } else {
      printf("0");
    }
  }
  return 0;
}
