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;
inline int gi() {
  int f = 1, sum = 0;
  char ch = getchar();
  while (ch > '9' || ch < '0') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    sum = (sum << 3) + (sum << 1) + ch - '0';
    ch = getchar();
  }
  return f * sum;
}
const int N = 200010, LG = 19;
int a[N], p[N], n, m, q, nxt[N][LG], pos[N], lst[N], ans[N], t[N << 2];
void build(int o, int l, int r) {
  if (l == r) {
    t[o] = ans[l];
    return;
  }
  int mid = (l + r) >> 1;
  build(o << 1, l, mid);
  build(o << 1 | 1, mid + 1, r);
  t[o] = min(t[o << 1], t[o << 1 | 1]);
}
int query(int o, int l, int r, int posl, int posr) {
  if (posl <= l && r <= posr) return t[o];
  int mid = (l + r) >> 1, ret = 1e9 + 10;
  if (posl <= mid) ret = min(ret, query(o << 1, l, mid, posl, posr));
  if (mid < posr) ret = min(ret, query(o << 1 | 1, mid + 1, r, posl, posr));
  return ret;
}
void init() {
  for (int i = 1; i <= n; i++) pos[p[i]] = i;
  p[n + 1] = p[1];
  nxt[m + 1][0] = m + 1;
  for (int i = m; i; i--) {
    int id = pos[a[i]];
    nxt[i][0] = lst[p[id + 1]] ? lst[p[id + 1]] : m + 1;
    lst[a[i]] = i;
  }
  for (int j = 1; j < LG; j++)
    for (int i = 1; i <= m + 1; i++) nxt[i][j] = nxt[nxt[i][j - 1]][j - 1];
  for (int i = 1; i <= m; i++) {
    int jump = i;
    for (int j = 0; j < LG; j++)
      if (((n - 1) >> j) & 1) jump = nxt[jump][j];
    ans[i] = jump;
  }
  build(1, 1, m);
}
int main() {
  n = gi();
  m = gi();
  q = gi();
  for (int i = 1; i <= n; i++) p[i] = gi();
  for (int i = 1; i <= m; i++) a[i] = gi();
  init();
  while (q--) {
    int l = gi(), r = gi();
    printf("%d", query(1, 1, m, l, r) <= r);
  }
  puts("");
  return 0;
}
