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>
const int N = (int)5e5 + 7;
const int inf = (int)1e9 + 7;
const int mod = (int)1e9 + 7;
const long long linf = (long long)1e18 + 7;
const int dx[] = {-1, 0, 1, 0, 1, -1, -1, 1};
const int dy[] = {0, 1, 0, -1, 1, -1, 1, -1};
using namespace std;
int n, m, q;
int p[N], a[N];
int go[N], last[N], nxt[N];
int up[N][20];
int jmp(int p) {
  int len = n - 1;
  for (int i = (19); i >= (0); i--) {
    if ((1 << i) <= len) {
      len -= (1 << i);
      p = up[p][i];
    }
  }
  return p;
}
struct tree {
  int t[N << 2];
  void build(int v = 1, int tl = 1, int tr = m) {
    if (tl == tr) {
      t[v] = jmp(tl);
      return;
    }
    int tm = tl + tr >> 1;
    build(v << 1, tl, tm);
    build(v << 1 | 1, tm + 1, tr);
    t[v] = min(t[v << 1], t[v << 1 | 1]);
  }
  int get(int l, int r, int v = 1, int tl = 1, int tr = m) {
    if (l <= tl && tr <= r) return t[v];
    if (tl > r || tr < l) return inf;
    int tm = tl + tr >> 1;
    return min(get(l, r, v << 1, tl, tm), get(l, r, v << 1 | 1, tm + 1, tr));
  }
} t;
int main() {
  ios_base ::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  cin >> n >> m >> q;
  for (int i = (1); i <= (n); i++) cin >> p[i];
  for (int i = (1); i <= (m); i++) cin >> a[i];
  for (int i = (1); i <= (n - 1); i++) go[p[i]] = p[i + 1];
  go[p[n]] = p[1];
  for (int i = (1); i <= (n); i++) last[i] = m + 1;
  for (int i = (0); i <= (19); i++) up[m + 1][i] = m + 1;
  for (int i = (m); i >= (1); i--) {
    up[i][0] = last[go[a[i]]];
    last[a[i]] = i;
  }
  for (int i = (1); i <= (19); i++) {
    for (int j = (1); j <= (m); j++) {
      up[j][i] = up[up[j][i - 1]][i - 1];
    }
  }
  t.build();
  for (int i = (1); i <= (q); i++) {
    int l, r;
    cin >> l >> r;
    if (t.get(l, r) <= r)
      cout << 1;
    else
      cout << 0;
  }
  exit(0);
}
