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 inf = (int)1.01e9;
const long long infll = (long long)1.01e18;
const long double eps = 1e-9;
const long double pi = acos((long double)-1);
mt19937 mrand(chrono::steady_clock::now().time_since_epoch().count());
int rnd(int x) { return mrand() % x; }
void precalc() {}
const int maxn = (int)2e5 + 5;
int n, m, q;
int p[maxn];
int a[maxn];
int ql[maxn], qr[maxn];
bool read() {
  if (scanf("%d%d%d", &n, &m, &q) < 3) {
    return false;
  }
  for (int i = 0; i < n; i++) {
    scanf("%d", &p[i]);
    p[i]--;
  }
  for (int i = 0; i < m; i++) {
    scanf("%d", &a[i]);
    a[i]--;
  }
  for (int i = 0; i < q; i++) {
    scanf("%d%d", &ql[i], &qr[i]);
    ql[i]--;
  }
  return true;
}
const int logn = 20;
int pp[maxn];
int lst[maxn];
int par[maxn][logn];
int rs[maxn];
int goUp(int v, int k) {
  for (int i = 0; i < logn; i++) {
    if (k & (1 << i)) {
      v = par[v][i];
    }
  }
  return v;
}
vector<int> qs[maxn];
string ans;
void solve() {
  for (int i = 0; i < n; i++) {
    pp[p[i]] = i;
  }
  for (int i = 0; i < n; i++) {
    lst[i] = m;
  }
  for (int i = 0; i < logn; i++) {
    par[m][i] = m;
  }
  for (int i = m - 1; i >= 0; i--) {
    int x = a[i];
    lst[x] = i;
    int y;
    {
      int pos = pp[x];
      pos = (pos + 1) % n;
      y = p[pos];
    }
    par[i][0] = lst[y];
    for (int j = 1; j < logn; j++) {
      par[i][j] = par[par[i][j - 1]][j - 1];
    }
    rs[i] = goUp(i, n - 1);
  }
  for (int i = 0; i < m; i++) {
    qs[i].clear();
  }
  for (int i = 0; i < q; i++) {
    qs[ql[i]].push_back(i);
  }
  ans = string(q, '0');
  int r = m;
  for (int i = m - 1; i >= 0; i--) {
    r = min(r, rs[i]);
    for (int j = 0; j < ((int)(qs[i]).size()); j++) {
      int id = qs[i][j];
      if (r < qr[id]) {
        ans[id] = '1';
      }
    }
  }
  printf("%s\n", ans.c_str());
}
int main() {
  precalc();
  while (read()) {
    solve();
  }
  return 0;
}
