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 + 15;
const int M = 18;
int in[N];
int lastInd[N], len[N];
int per[N], perInd[N];
int jump[N][M];
int minDist[N];
int seg[N * 4];
void init(int pos, int l, int r) {
  if (l == r) {
    seg[pos] = minDist[l];
    return;
  }
  int mid = (l + r) / 2;
  init(pos * 2, l, mid);
  init(pos * 2 + 1, mid + 1, r);
  seg[pos] = min(seg[pos * 2], seg[pos * 2 + 1]);
}
int query(int pos, int l, int r, int ql, int qr) {
  if (r < ql || qr < l) {
    return 1e9;
  }
  if (ql <= l && r <= qr) {
    return seg[pos];
  }
  int mid = (l + r) / 2;
  return min(query(pos * 2, l, mid, ql, qr),
             query(pos * 2 + 1, mid + 1, r, ql, qr));
}
void solve() {
  int n, m, q;
  scanf("%d %d %d", &n, &m, &q);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &per[i]);
    perInd[per[i]] = i;
  }
  for (int i = 1; i <= m; ++i) {
    scanf("%d", &in[i]);
  }
  memset(lastInd, -1, sizeof(lastInd));
  for (int i = m; i >= 1; --i) {
    minDist[i] = 1e9;
    int curPerInd = perInd[in[i]];
    int nextInd = curPerInd + 1;
    if (nextInd > n) {
      nextInd -= n;
    }
    nextInd = lastInd[per[nextInd]];
    if (nextInd == -1) {
      len[i] = 1;
    } else {
      len[i] = min(n, len[nextInd] + 1);
      jump[i][0] = nextInd;
      for (int j = 1; j < M; ++j) {
        jump[i][j] = jump[jump[i][j - 1]][j - 1];
      }
    }
    if (len[i] == n) {
      int cur = i, d = n - 1;
      for (int j = 0; j < M; ++j) {
        if (d & (1 << j)) {
          cur = jump[cur][j];
        }
      }
      minDist[i] = cur;
    }
    lastInd[in[i]] = i;
  }
  init(1, 1, m);
  for (int i = 0; i < q; ++i) {
    int l, r;
    scanf("%d %d", &l, &r);
    int q = query(1, 1, m, l, r);
    if (q <= r) {
      printf("1");
    } else {
      printf("0");
    }
  }
  cout << endl;
}
int main() { solve(); }
