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 = 2e5 + 10;
int n, m;
int p[maxn], a[maxn], pre[maxn], pos[maxn], go[maxn];
int fa[maxn][20];
pair<int, int> q[maxn];
int jump(int x) {
  int now = x;
  for (int i = 19; i >= 0; i--) {
    if ((n - 1) & (1 << i)) {
      now = fa[now][i];
    }
  }
  return now;
}
void init() {
  pre[p[1]] = p[n];
  for (int i = 2; i <= n; i++) {
    pre[p[i]] = p[i - 1];
  }
  for (int i = 1; i <= m; i++) {
    int last = pre[a[i]];
    if (pos[last]) {
      fa[i][0] = pos[last];
    }
    pos[a[i]] = i;
  }
  for (int j = 1; j < 20; j++) {
    for (int i = 1; i <= m; i++) {
      fa[i][j] = fa[fa[i][j - 1]][j - 1];
    }
  }
  for (int i = 1; i <= m; i++) {
    go[i] = jump(i);
  }
}
int Max[maxn << 2];
void build(int o, int l, int r) {
  if (l == r) {
    Max[o] = go[l];
    return;
  }
  int mid = l + r >> 1;
  build(o << 1, l, mid);
  build(o << 1 | 1, mid + 1, r);
  Max[o] = max(Max[o << 1], Max[o << 1 | 1]);
}
int query(int o, int l, int r, int ql, int qr) {
  if (ql <= l && r <= qr) {
    return Max[o];
  }
  int mid = l + r >> 1;
  int ans1 = -1, ans2 = -1;
  if (ql <= mid) ans1 = query(o << 1, l, mid, ql, qr);
  if (qr > mid) ans2 = query(o << 1 | 1, mid + 1, r, ql, qr);
  return max(ans1, ans2);
}
bool solve(int l, int r) {
  int Max = query(1, 1, m, l, r);
  if (Max >= l && Max <= r)
    return true;
  else
    return false;
}
int main(int argc, char const *argv[]) {
  ios::sync_with_stdio(false);
  int qq;
  cin >> n >> m >> qq;
  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 <= qq; i++) cin >> q[i].first >> q[i].second;
  init();
  build(1, 1, m);
  for (int i = 1; i <= qq; i++) {
    if (solve(q[i].first, q[i].second))
      printf("1");
    else
      printf("0");
  }
  puts("");
  return 0;
}
