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 = 200000;
const int MaxLogN = 19;
int n, m;
int pe[MaxN + 1], a[MaxN + 1];
struct node {
  int cnt;
  node *lc, *rc;
};
int n_nodes = 0;
node pool[MaxN * MaxLogN];
node *tr[MaxN + 1];
node *node_insert(node *p, int pL, int pR, int pV) {
  node *np = pool + (n_nodes++);
  if (p) *np = *p;
  np->cnt++;
  if (pL == pR) return np;
  int pM = (pL + pR) >> 1;
  if (pV <= pM)
    np->lc = node_insert(np->lc, pL, pM, pV);
  else
    np->rc = node_insert(np->rc, pM + 1, pR, pV);
  return np;
}
int node_query(node *p1, node *p2, int pL, int pR, int qR) {
  if (!p1 && !p2) return 0;
  if (pR <= qR) {
    int cnt1 = p1 ? p1->cnt : 0;
    int cnt2 = p2 ? p2->cnt : 0;
    return cnt1 - cnt2;
  }
  int pM = (pL + pR) >> 1;
  int cur = node_query(p1 ? p1->lc : NULL, p2 ? p2->lc : NULL, pL, pM, qR);
  if (pM <= qR)
    cur += node_query(p1 ? p1->rc : NULL, p2 ? p2->rc : NULL, pM + 1, pR, qR);
  return cur;
}
void prepare() {
  static int next[MaxN + 1];
  for (int i = 1; i <= n; i++) next[pe[i]] = pe[i % n + 1];
  static int pos[MaxN + 1];
  static int fa[MaxN + 1][MaxLogN + 1];
  static int g[MaxN + 1];
  for (int i = m; i >= 1; i--) {
    fa[i][0] = pos[next[a[i]]];
    pos[a[i]] = i;
    for (int j = 0; fa[i][j]; j++) fa[i][j + 1] = fa[fa[i][j]][j];
    g[i] = i;
    for (int j = MaxLogN; j >= 0 && g[i]; j--)
      if ((n - 1) >> j & 1) g[i] = fa[g[i]][j];
  }
  for (int i = 1; i <= m; i++) {
    if (g[i])
      tr[i] = node_insert(tr[i - 1], 1, m, g[i]);
    else
      tr[i] = tr[i - 1];
  }
}
int main() {
  int nQ;
  cin >> n >> m >> nQ;
  for (int i = 1; i <= n; i++) scanf("%d", &pe[i]);
  for (int i = 1; i <= m; i++) scanf("%d", &a[i]);
  prepare();
  while (nQ--) {
    int qL, qR;
    scanf("%d %d", &qL, &qR);
    if (node_query(tr[qR], tr[qL - 1], 1, m, qR))
      putchar('1');
    else
      putchar('0');
  }
  cout << endl;
  return 0;
}
