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;
vector<int> p, a, nextInP, ans;
int nextInA[(int)2e5 + 10][20];
int n, m, q;
vector<vector<int> > indicesOf;
const int LOGN = 18, N = 1 << LOGN;
int rm[LOGN][N];
int getNextInA(int curInd) {
  if (curInd == m) return m;
  int nextElem = nextInP[a[curInd]];
  int ret = *lower_bound(indicesOf[nextElem].begin(), indicesOf[nextElem].end(),
                         curInd);
  return ret;
}
void getFirstLevel() {
  for (int i = 0; i <= m; i++) {
    nextInA[i][0] = getNextInA(i);
  }
}
void getAllLevels() {
  for (int steps = 1; steps < 20; steps++) {
    for (int i = 0; i <= m; i++) {
      nextInA[i][steps] = nextInA[nextInA[i][steps - 1]][steps - 1];
    }
  }
}
void getAllNearest() {
  int steps = n - 1;
  for (int start = 0; start < m; start++) {
    int cur = start;
    for (int i = 0; i < 20; i++) {
      if ((steps & (1 << i)) != 0) {
        cur = nextInA[cur][i];
      }
    }
    ans[start] = cur;
  }
}
int LeadingZeros[(int)(2e5) + 10];
void LZ(int n) {
  int Lzeros = 31;
  int j = 1;
  for (int i = 1; i <= n; i = (i << 1)) {
    while (j < (i << 1) && j <= n) {
      LeadingZeros[j] = Lzeros;
      j++;
    }
    Lzeros--;
  }
}
void init(vector<int> tab, int n) {
  LZ(n);
  for (int i = 0; i < n; i++) rm[0][i] = tab[i];
  for (int k = 1; k < LOGN; k++)
    for (int i = 0; i <= n - (1 << k); i++)
      rm[k][i] = std::min(rm[k - 1][i], rm[k - 1][i + (1 << (k - 1))]);
}
int query(int a, int b) {
  int k = 31 - LeadingZeros[b - a + 1];
  return std::min(rm[k][a], rm[k][b - (1 << k) + 1]);
}
int ansQuery(int l, int r) { return (query(l, r) <= r); }
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0), cout.tie(0);
  cin >> n >> m >> q;
  p.resize(n);
  indicesOf.resize(n);
  nextInP.resize(n);
  a.resize(m);
  ans.resize(m);
  for (int i = 0; i < n; i++) {
    cin >> p[i];
    p[i]--;
  }
  for (int i = 0; i < n; i++) {
    nextInP[p[i]] = p[(i + 1) % n];
  }
  for (int i = 0; i < m; i++) {
    cin >> a[i];
    a[i]--;
    indicesOf[a[i]].push_back(i);
  }
  for (int i = 0; i < n; i++) {
    indicesOf[i].push_back(m);
  }
  getFirstLevel();
  getAllLevels();
  getAllNearest();
  init(ans, m);
  while (q--) {
    int li, ri;
    cin >> li >> ri;
    li--;
    ri--;
    cout << ansQuery(li, ri);
  }
  cout << "\n";
  return 0;
}
