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 N = 2e5 + 10;
struct data {
  int l, r, id;
} d[N], c[N];
struct node {
  int ss, r;
};
struct Gei {
  int r, id;
  bool operator<(const Gei &C) const { return r < C.r; }
};
vector<node> v[N];
priority_queue<Gei> Q;
int qz[N], hz[N], ans[N];
int a[N], mk[N];
bool cmp(data xx, data yy) {
  if (xx.l != yy.l)
    return xx.l < yy.l;
  else
    return xx.r < yy.r;
}
int main() {
  int n, m, q;
  scanf("%d%d%d", &n, &m, &q);
  for (int i = 1; i <= n; ++i) {
    int x;
    scanf("%d", &x);
    mk[x] = i;
  }
  for (int i = 1; i <= m; ++i) scanf("%d", &a[i]);
  memset(qz, -1, sizeof qz), memset(hz, -1, sizeof hz);
  for (int i = 1; i <= m; ++i) {
    int sit = mk[a[i]];
    if (sit == 1)
      qz[sit] = i;
    else
      qz[sit] = qz[sit - 1];
    if (qz[sit] != -1) v[sit].push_back((node){i, qz[sit]});
  }
  int res = 0;
  for (int i = m; i >= 1; --i) {
    int sit = mk[a[i]];
    if (sit == n)
      hz[sit] = i;
    else
      hz[sit] = hz[sit + 1];
    if (hz[sit] != -1) {
      if (sit == 1) {
        c[++res].l = i, c[res].r = hz[sit];
        continue;
      }
      int len = v[sit - 1].size();
      if (!len || v[sit - 1][len - 1].r < hz[sit]) continue;
      int l = 0, r = len - 1, tt = -1;
      while (l <= r) {
        int mid = (l + r) >> 1;
        if (v[sit - 1][mid].r >= hz[sit])
          r = mid - 1, tt = mid;
        else
          l = mid + 1;
      }
      c[++res].l = i, c[res].r = v[sit - 1][tt].ss;
    }
  }
  for (int i = 1; i <= q; ++i) scanf("%d%d", &d[i].l, &d[i].r), d[i].id = i;
  sort(c + 1, c + 1 + res, cmp), sort(d + 1, d + 1 + q, cmp);
  int head = 1, tail = 0, lt = 0;
  for (int i = 1; i <= res; ++i) {
    while (lt + 1 <= q && d[lt + 1].l <= c[i].l)
      lt++, Q.push((Gei){d[lt].r, d[lt].id});
    while (Q.size() && Q.top().r >= c[i].r) {
      Gei h = Q.top();
      Q.pop();
      ans[h.id] = 1;
    }
  }
  for (int i = 1; i <= q; ++i) printf("%d", ans[i]);
  return 0;
}
