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;
int tree[200010 * 4];
void update(int idx, int b, int e, int p, int v) {
  if (b > p || p > e) return;
  if (b == e) {
    tree[idx] = v;
    return;
  }
  int m = (b + e) >> 1;
  update((idx << 1), b, m, p, v);
  update(((idx << 1) + 1), m + 1, e, p, v);
  tree[idx] = min(tree[(idx << 1)], tree[((idx << 1) + 1)]);
}
int query(int idx, int b, int e, int l, int r) {
  if (b > r || e < l) return 200010;
  if (l <= b && e <= r) return tree[idx];
  int m = (b + e) >> 1;
  return min(query((idx << 1), b, m, l, r),
             query(((idx << 1) + 1), m + 1, e, l, r));
}
int n, m, q, per[200010], ara[200010], nex[200010], go[200010];
vector<int> mat[200010];
int vis[200010], dfa[200010], ti, rev[200010], extraHead[200010],
    twoPos[200010];
int dfs(int p, int col) {
  dfa[ti] = p;
  vis[p] = col;
  rev[p] = ti;
  ti++;
  for (auto x : mat[p]) {
    if (vis[x]) return extraHead[p] = x;
    extraHead[p] = dfs(x, col);
  }
  return extraHead[p];
}
int getDis(int x, int y) {
  if (twoPos[x] < twoPos[y])
    return twoPos[y] - twoPos[x];
  else
    return n + twoPos[y] - twoPos[x];
}
int getPos(int p, int jump) {
  int x = rev[p] + jump;
  if (x < m) x = dfa[x];
  if (rev[p] + jump < m && vis[x] == vis[p])
    return x;
  else if (extraHead[p] != -1) {
    int myCol = ara[p], hisCol = ara[extraHead[p]];
    int dis = getDis(myCol, hisCol);
    return getPos(extraHead[p], jump - dis);
  } else
    return -1;
}
int main() {
  ios::sync_with_stdio(false);
  int u, v;
  cin >> n >> m >> q;
  for (int i = 0; i <= n - 1; i++) cin >> per[i], twoPos[per[i]] = i;
  for (int i = 0; i <= m - 1; i++) cin >> ara[i];
  for (int i = 0; i <= n - 1; i++) {
    if (i != n - 1)
      go[per[i]] = per[i + 1];
    else
      go[per[n - 1]] = per[0];
  }
  memset(nex, -1, sizeof(nex));
  memset(extraHead, -1, sizeof(extraHead));
  for (int i = m - 1; i >= 0; i--) {
    int u = ara[i], v = go[u];
    v = nex[v];
    if (v != -1) mat[i].push_back(v);
    nex[u] = i;
  }
  for (int i = 0; i <= m - 1; i++) {
    if (vis[i]) continue;
    dfs(i, i + 1);
  }
  for (int i = 0; i <= m - 1; i++) {
    int v = getPos(i, n - 1);
    if (v == -1) v = 200010;
    update(1, 0, 200010, i, v);
  }
  int l, r;
  for (int i = 1; i <= q; i++) {
    cin >> l >> r;
    l--;
    r--;
    if (query(1, 0, 200010, l, r) <= r)
      cout << 1;
    else
      cout << 0;
  }
  return 0;
}
