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 = (int)2e5 + 50;
int n, m, q, p[maxn], pos[maxn], la[maxn], f[maxn][25], st[maxn];
int leaf[maxn];
struct X {
  int l, r, maxx;
} tree[4 * maxn];
void BuildTree(int id, int le, int ri) {
  tree[id].l = le;
  tree[id].r = ri;
  tree[id].maxx = 0;
  if (le == ri) {
    leaf[le] = id;
    return;
  }
  int mid = (le + ri) / 2;
  BuildTree(id * 2, le, mid);
  BuildTree(id * 2 + 1, mid + 1, ri);
}
void Up(int id, int val) {
  tree[id].maxx = val;
  id /= 2;
  while (id) {
    tree[id].maxx = max(tree[id * 2].maxx, tree[id * 2 + 1].maxx);
    id /= 2;
  }
}
int Get(int id, int u, int v) {
  if (tree[id].l > v || tree[id].r < u) return 0;
  if (tree[id].l >= u && tree[id].r <= v) return tree[id].maxx;
  return max(Get(id * 2, u, v), Get(id * 2 + 1, u, v));
}
int main() {
  cin >> n >> m >> q;
  for (int i = 1; i <= n; ++i) {
    cin >> p[i];
    pos[p[i]] = i;
  }
  memset(f, -1, sizeof(f));
  memset(la, -1, sizeof(la));
  for (int i = 1; i <= m; ++i) {
    int a;
    cin >> a;
    int pre;
    if (pos[a] > 1)
      pre = p[pos[a] - 1];
    else
      pre = p[n];
    f[i][0] = la[pre];
    la[a] = i;
  }
  for (int j = 1; 1 << j <= m; ++j) {
    for (int i = 1; i <= m; ++i) {
      if (f[i][j - 1] != -1) f[i][j] = f[f[i][j - 1]][j - 1];
    }
  }
  BuildTree(1, 1, m);
  for (int i = 1; i <= m; ++i) {
    int u = i;
    int h = n - 1;
    for (int j = 20; j >= 0; --j) {
      if (f[u][j] != -1 && (h - (1 << j)) >= 0) {
        u = f[u][j];
        h -= (1 << j);
      }
    }
    if (h == 0) Up(leaf[i], u);
  }
  for (int i = 1; i <= q; ++i) {
    int l, r;
    cin >> l >> r;
    int ma = Get(1, l, r);
    if (ma < l)
      cout << 0;
    else
      cout << 1;
  }
}
