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 <typename T>
string tos(T a) {
  stringstream ss;
  string ret;
  ss << a;
  ss >> ret;
  return ret;
}
void read(int &_a) { int temp = scanf("%d", &_a); }
void read(int &_a, int &_b) { int temp = scanf("%d %d", &_a, &_b); }
void read(int &_a, int &_b, int &_c) {
  int temp = scanf("%d %d %d", &_a, &_b, &_c);
}
const int SZ = 2e5 + 7;
int N, M, Q;
int P[SZ], A[SZ], T[SZ], TX[SZ][20];
int PX[SZ], AX[SZ], MXR[SZ];
int getp(int u, int n) {
  int lg = 1;
  while ((1 << lg) <= n) lg++;
  lg--;
  for (int i = lg; i >= 0; i--) {
    if (u == -1) break;
    if ((1 << i) <= n) {
      n -= (1 << i);
      u = TX[u][i];
    }
  }
  return u;
}
int main() {
  while (cin >> N >> M >> Q) {
    memset(T, -1, sizeof T);
    ;
    memset(TX, -1, sizeof TX);
    ;
    memset(AX, -1, sizeof AX);
    ;
    for (int(x) = (0); (x) < (N); (x)++) {
      read(P[x]);
      PX[P[x]] = x;
    }
    for (int(x) = (0); (x) < (M); (x)++) {
      read(A[x]);
      int li = PX[A[x]];
      li = (li - 1 + N) % N;
      int pv = P[li];
      if (AX[pv] != -1) T[x] = AX[pv];
      AX[A[x]] = x;
    }
    for (int(x) = (0); (x) < (M); (x)++) TX[x][0] = T[x];
    for (int j = 1; (1 << j) <= M; j++) {
      for (int(i) = (0); (i) < (M); (i)++) {
        if (TX[i][j - 1] != -1) {
          TX[i][j] = TX[TX[i][j - 1]][j - 1];
        }
      }
    }
    int mx = -1;
    for (int(x) = (0); (x) < (M); (x)++) {
      int lf = getp(x, N - 1);
      mx = max(mx, lf);
      MXR[x] = mx;
    }
    string ans = "";
    int la, lb;
    for (int(q) = (0); (q) < (Q); (q)++) {
      read(la, lb);
      la--;
      lb--;
      int lf = MXR[lb];
      if (lf >= la)
        ans += "1";
      else
        ans += "0";
    }
    cout << ans << endl;
  }
  return 0;
}
