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 long long INF = 2147483647;
const long long MOD = 1000000007;
const long long mod = 998244353;
const long double eps = 1e-12;
long long n, m, q;
long long perm[200001];
long long arr[200001];
long long nextperm[200001];
set<long long> pos[200001];
long long dp[200001][20];
long long ed[200001];
struct Node {
  long long sl, sr;
  long long Min;
};
Node st[800001];
void build(long long cidx, long long cl, long long cr) {
  st[cidx].sl = cl;
  st[cidx].sr = cr;
  if (cl < cr) {
    long long mid = (cl + cr) / 2;
    build(cidx * 2, cl, mid);
    build(cidx * 2 + 1, mid + 1, cr);
    st[cidx].Min = min(st[cidx * 2].Min, st[cidx * 2 + 1].Min);
  } else {
    st[cidx].Min = ed[cl];
  }
}
long long query(long long cidx, long long ql, long long qr) {
  long long cl = st[cidx].sl;
  long long cr = st[cidx].sr;
  if (qr < cl or cr < ql) return INF;
  if (ql <= cl and cr <= qr) return st[cidx].Min;
  return min(query(cidx * 2, ql, qr), query(cidx * 2 + 1, ql, qr));
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m >> q;
  for (long long i = 0; i < n; i++) {
    cin >> perm[i];
    perm[i]--;
  }
  for (long long i = 0; i < m; i++) {
    cin >> arr[i];
    arr[i]--;
  }
  for (long long i = 0; i < n; i++) {
    nextperm[perm[i]] = perm[(i + 1) % n];
  }
  for (long long i = 0; i < m; i++) {
    pos[arr[i]].insert(i);
  }
  for (long long i = 0; i < n; i++) {
    pos[i].insert(INF);
  }
  for (long long i = 0; i < m; i++) {
    dp[i][0] = *(pos[nextperm[arr[i]]].lower_bound(i + 1));
  }
  for (long long j = 1; j <= 19; j++) {
    for (long long i = 0; i < m; i++) {
      if (dp[i][j - 1] == INF)
        dp[i][j] = INF;
      else
        dp[i][j] = dp[dp[i][j - 1]][j - 1];
    }
  }
  for (long long i = 0; i < m; i++) {
    long long dis = n - 1;
    long long ptr = i;
    for (long long j = 0; j <= 19; j++) {
      if ((dis & (1 << j)) != 0) {
        if (ptr == INF) continue;
        ptr = dp[ptr][j];
      }
    }
    ed[i] = ptr;
  }
  build(1, 0, m - 1);
  long long ql, qr;
  while (q--) {
    cin >> ql >> qr;
    ql--;
    qr--;
    if (query(1, ql, qr) <= qr)
      cout << 1;
    else
      cout << 0;
  }
  cout << endl;
  return 0;
}
