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 N = 2e5;
int p[N + 10], a[N + 10], pos[N + 10];
struct seg {
  int l, r, min;
} t[N * 4 + 10];
int nxt[N + 10][20];
int get(int x, int n) {
  int ans = x, cnt = 0;
  while (n) {
    if (n & 1) ans = nxt[ans][cnt];
    if (ans >= 0x7f7f7f7f) break;
    n >>= 1;
    cnt++;
  }
  return ans;
}
int n;
void build(int p, int l, int r) {
  t[p].l = l;
  t[p].r = r;
  if (l == r) {
    t[p].min = get(l, n - 1);
    return;
  }
  int mid = (l + r) / 2;
  build(p * 2, l, mid);
  build(p * 2 + 1, mid + 1, r);
  t[p].min = min(t[p * 2].min, t[p * 2 + 1].min);
}
int query(int p, int l, int r) {
  if (l <= t[p].l && t[p].r <= r) return t[p].min;
  int mid = (t[p].l + t[p].r) / 2, ans = 0x7f7f7f7f;
  if (l <= mid) ans = min(ans, query(p * 2, l, r));
  if (r > mid) ans = min(ans, query(p * 2 + 1, l, r));
  return ans;
}
int ans[N + 10];
int main() {
  int m, q;
  scanf("%d%d%d", &n, &m, &q);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &p[i]);
    pos[p[i]] = i;
  }
  for (int i = 1; i <= m; i++) {
    scanf("%d", &a[i]);
    a[i] = pos[a[i]];
  }
  memset(pos, 0x7f, sizeof(pos));
  for (int i = m; i; i--) {
    nxt[i][0] = pos[a[i] == n ? 1 : a[i] + 1];
    pos[a[i]] = i;
  }
  int logn = (int)(log(n) / log(2)) + 1;
  for (int s = 1; s <= logn; s++) {
    for (int i = 1; i <= m; i++) {
      if (i + (1 << s) - 1 > m) {
        nxt[i][s] = 0x7f7f7f7f;
        continue;
      }
      if (nxt[i][s - 1] > m) {
        nxt[i][s] = 0x7f7f7f7f;
        continue;
      }
      nxt[i][s] = nxt[nxt[i][s - 1]][s - 1];
    }
  }
  build(1, 1, m);
  for (int i = 1; i <= q; i++) {
    int l, r;
    scanf("%d%d", &l, &r);
    int tmp = query(1, l, r);
    ans[i] = (tmp <= r);
  }
  for (int i = 1; i <= q; i++) putchar(48 ^ ans[i]);
}
