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 P = 1e9 + 7, INF = 0x3f3f3f3f;
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
long long qpow(long long a, long long n) {
  long long r = 1 % P;
  for (a %= P; n; a = a * a % P, n >>= 1)
    if (n & 1) r = r * a % P;
  return r;
}
long long inv(long long first) {
  return first <= 1 ? 1 : inv(P % first) * (P - P / first) % P;
}
const int N = 1e6 + 10;
int n, m, q, a[N], b[N], f[N], fa[N][21], pre[N], v[N << 2];
int Log[N];
int get(int first, int k) {
  while (k) first = fa[first][Log[k & -k]], k ^= k & -k;
  return first ? first : INF;
}
int build(int o, int l, int r) {
  if (l == r) return v[o] = get(l, n - 1);
  return v[o] = min(build((o << 1), l, ((l + r) >> 1)),
                    build(((o << 1) | 1), ((l + r) >> 1) + 1, r));
}
int query(int o, int l, int r, int ql, int qr) {
  if (ql <= l && r <= qr) return v[o];
  if (((l + r) >> 1) >= qr) return query((o << 1), l, ((l + r) >> 1), ql, qr);
  if (((l + r) >> 1) < ql)
    return query(((o << 1) | 1), ((l + r) >> 1) + 1, r, ql, qr);
  return min(query((o << 1), l, ((l + r) >> 1), ql, qr),
             query(((o << 1) | 1), ((l + r) >> 1) + 1, r, ql, qr));
}
int main() {
  for (int i = 0; i <= 19; ++i) Log[1 << i] = i;
  scanf("%d%d%d", &n, &m, &q);
  if (n == 1) {
    for (int i = 1; i <= q; ++i) putchar('1');
    return putchar(10), 0;
  }
  for (int i = 1; i <= n; ++i) scanf("%d", a + i);
  for (int i = 1; i <= n; ++i) f[a[i]] = a[i + 1];
  f[a[n]] = a[1];
  for (int i = 1; i <= m; ++i) scanf("%d", b + i);
  for (int i = 1; i <= N - 1; ++i) pre[i] = N - 1;
  for (int i = m; i >= 1; --i) {
    fa[i][0] = pre[f[b[i]]];
    pre[b[i]] = i;
    for (int j = 1; j <= 20; ++j) fa[i][j] = fa[fa[i][j - 1]][j - 1];
  }
  build(1, 1, m);
  for (int i = 1; i <= q; ++i) {
    int first, second;
    scanf("%d%d", &first, &second);
    putchar(query(1, 1, m, first, second) <= second ? '1' : '0');
  }
  putchar(10);
}
