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;
const int MAXN = 2 * 105000;
class SegmentTree {
 private:
  const long long INF = 1e18;
  vector<long long> tree;
  int n;

 public:
  void init(int sz) {
    n = 1;
    while (n < sz) {
      n *= 2;
    }
    tree.assign(2 * n, INF);
  }
  long long getMin(int l, int r) {
    l = n + l;
    r = n + r;
    long long res = INF;
    while (l <= r) {
      if (l & 1) {
        res = min(res, tree[l]);
        l++;
      }
      if (r % 2 == 0) {
        res = min(res, tree[r]);
        r--;
      }
      l /= 2;
      r /= 2;
    }
    return res;
  }
  void update(int pos, long long val) {
    pos = n + pos;
    tree[pos] = val;
    pos /= 2;
    while (pos >= 1) {
      tree[pos] = min(tree[pos * 2], tree[pos * 2 + 1]);
      pos /= 2;
    }
  }
};
int n, m, qn;
int p[MAXN];
int a[MAXN];
int nxt[MAXN];
int nxtPos[MAXN];
int lastPos[MAXN];
int go[MAXN][20];
int main() {
  scanf("%d %d %d", &n, &m, &qn);
  for (int i = 0; i < n; i++) {
    scanf("%d", &p[i]);
    p[i]--;
  }
  for (int i = 0; i < m; i++) {
    scanf("%d", &a[i]);
    a[i]--;
  }
  for (int i = 0; i < n; i++) nxt[p[i]] = p[(i + 1) % n];
  for (int i = 0; i < n; i++) lastPos[i] = m;
  for (int i = m - 1; i >= 0; i--) {
    nxtPos[i] = lastPos[nxt[a[i]]];
    lastPos[a[i]] = i;
  }
  for (int i = 0; i < 20; i++) go[m][i] = m;
  for (int i = m - 1; i >= 0; i--) {
    for (int j = 0; j < 20; j++) {
      if (j == 0) {
        go[i][j] = nxtPos[i];
      } else {
        go[i][j] = go[go[i][j - 1]][j - 1];
      }
    }
  }
  SegmentTree tree;
  tree.init(m);
  for (int i = 0; i < m; i++) {
    int need = n - 1;
    int pos = i;
    for (int j = 19; j >= 0; j--) {
      while (need >= (1 << j)) {
        need -= (1 << j);
        pos = go[pos][j];
      }
    }
    tree.update(i, pos);
  }
  string ans(qn, '0');
  for (int i = 0; i < qn; i++) {
    int l, r;
    scanf("%d %d", &l, &r);
    l--;
    r--;
    int mn = tree.getMin(l, r);
    if (mn <= r)
      ans[i] = '1';
    else
      ans[i] = '0';
  }
  cout << ans << endl;
  return 0;
}
