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;
struct segtree {
  vector<int> seg;
  int size;
  int neutro;
  int f(int a, int b) { return min(a, b); }
  segtree(vector<int> &v, int neu = 0) {
    int n = 1;
    while (n < v.size()) n = n << 1;
    seg.assign(2 * n, neu);
    size = n;
    neutro = neu;
    build(v, 0, 0, size);
  }
  void build(vector<int> &v, int x, int lx, int rx) {
    if (rx - lx == 1) {
      if (lx < v.size()) seg[x] = v[lx];
      return;
    }
    int mid = lx + (rx - lx) / 2;
    build(v, 2 * x + 1, lx, mid);
    build(v, 2 * x + 2, mid, rx);
    seg[x] = f(seg[2 * x + 1], seg[2 * x + 2]);
  }
  void set(int index, int valor, int x, int lx, int rx) {
    if (rx - lx == 1) {
      seg[x] = valor;
      return;
    }
    int mid = lx + (rx - lx) / 2;
    if (index < mid) {
      set(index, valor, 2 * x + 1, lx, mid);
    } else {
      set(index, valor, 2 * x + 2, mid, rx);
    }
    seg[x] = f(seg[2 * x + 1], seg[2 * x + 2]);
  }
  void set(int index, int valor) { set(index, valor, 0, 0, size); }
  int query(int l, int r, int x, int lx, int rx) {
    if (r <= lx || l >= rx) return neutro;
    if (lx >= l && rx <= r) return seg[x];
    int mid = lx + (rx - lx) / 2;
    return f(query(l, r, 2 * x + 1, lx, mid), query(l, r, 2 * x + 2, mid, rx));
  }
  int query(int l, int r) { return query(l, r, 0, 0, size); }
};
const int maxn = 2e5 + 10;
const int maxlog = 20;
int perm[maxn];
int v[maxn];
int prox[maxn];
int pai[maxn];
int dp[maxn][maxlog];
int jmp(int a, int j) {
  for (int i = 0; i < maxlog; i++)
    if ((j >> i) & 1) a = dp[a][i];
  return a;
}
int main() {
  int n, m, q;
  cin >> n >> m >> q;
  vector<int> perm(n);
  for (auto &k : perm) cin >> k;
  unordered_map<int, int> anterior;
  unordered_map<int, int> lastap;
  for (int i = 1; i < n; i++) {
    anterior[perm[i - 1]] = perm[i];
  }
  anterior[perm[perm.size() - 1]] = perm[0];
  for (int i = 1; i <= m; i++) cin >> v[i];
  for (int i = m; i > 0; i--) {
    pai[i] = lastap[anterior[v[i]]];
    lastap[v[i]] = i;
  }
  for (int i = 0; i < maxn; i++) {
    dp[i][0] = pai[i];
  }
  for (int j = 1; j < maxlog; j++)
    for (int i = 0; i < maxn; i++) dp[i][j] = dp[dp[i][j - 1]][j - 1];
  vector<int> proximo(m + 1);
  for (int i = 1; i <= m; i++) {
    proximo[i] = jmp(i, n - 1);
  }
  for (auto &k : proximo)
    if (k == 0) k = INT_MAX;
  segtree seg1 = segtree(proximo, INT_MAX);
  while (q--) {
    int a, b;
    cin >> a >> b;
    if (seg1.query(a, b + 1) <= b)
      cout << 1;
    else
      cout << 0;
  }
  cout << endl;
}
