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 segment_tree {
  int val[200005 << 2];
  inline void update(int l, int r, int k, int x, int w) {
    if (l == r) {
      val[k] = w;
      return;
    }
    int mid = l + r >> 1;
    if (x <= mid)
      update(l, mid, k << 1, x, w);
    else
      update(mid + 1, r, k << 1 | 1, x, w);
    val[k] = max(val[k << 1], val[k << 1 | 1]);
  }
  inline int query(int l, int r, int k, int L, int R) {
    if (L <= l && r <= R) return val[k];
    int mid = l + r >> 1, ans = 0;
    if (L <= mid) ans = max(ans, query(l, mid, k << 1, L, R));
    if (mid < R) ans = max(ans, query(mid + 1, r, k << 1 | 1, L, R));
    return ans;
  }
} sgt;
int p[200005], pos[200005], a[200005], lg2[200005];
int lastp[200005], pre[200005][20];
char str[200005];
int main() {
  int n, m, q;
  scanf("%d%d%d", &n, &m, &q);
  lg2[1] = 0;
  for (int i = 2; i <= m; i++) lg2[i] = lg2[i >> 1] + 1;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &p[i]);
    pos[p[i]] = i;
  }
  p[n + 1] = p[1], p[0] = p[n];
  for (int i = 1; i <= m; i++) {
    scanf("%d", &a[i]);
    pre[i][0] = lastp[p[pos[a[i]] - 1]];
    for (int k = 1; k <= lg2[i]; k++) pre[i][k] = pre[pre[i][k - 1]][k - 1];
    lastp[a[i]] = i;
  }
  for (int i = 1; i <= m; i++) {
    int x = i, k = n - 1;
    while (k) {
      x = pre[x][lg2[k]];
      k -= 1 << lg2[k];
    }
    if (x) sgt.update(1, m, 1, i, x);
  }
  for (int i = 1; i <= q; i++) {
    int l, r;
    scanf("%d%d", &l, &r);
    int t = sgt.query(1, m, 1, l, r);
    if (t >= l)
      str[i] = '1';
    else
      str[i] = '0';
  }
  str[q + 1] = '\0';
  puts(str + 1);
  return 0;
}
