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;
mt19937 rnd(chrono::high_resolution_clock::now().time_since_epoch().count());
const int maxn = 4e5 + 10;
int n, m, q, a[maxn], p[maxn], mp[maxn];
int nxt[maxn], pos[maxn], to[maxn];
int lg[maxn], val[18][maxn];
void build() {
  for (int i = (1), iend = (m); i <= iend; ++i) val[0][i] = to[i];
  for (int i = 2; i <= m; i++) {
    lg[i] = lg[i >> 1] + 1;
  }
  for (int i = 1; i < 18; i++) {
    for (int j = 1; j + (1 << i) - 1 <= m; j++) {
      val[i][j] = min(val[i - 1][j], val[i - 1][j + (1 << (i - 1))]);
    }
  }
}
int query(int l, int r) {
  int k = lg[r - l + 1];
  return min(val[k][l], val[k][r - (1 << k) + 1]);
}
namespace GETto {
int deg[maxn], dep[maxn], fa[18][maxn];
vector<int> e[maxn];
int query(int u) {
  int k = n - 1;
  if (dep[u] <= k) return m + 1;
  for (int i = 17; ~i; i--) {
    if (k >> i & 1) u = fa[i][u];
  }
  return u;
}
void dfs(int u) {
  for (int i = 1; i < 18; i++) {
    fa[i][u] = fa[i - 1][fa[i - 1][u]];
  }
  to[u] = query(u);
  for (int v : e[u]) {
    fa[0][v] = u;
    dep[v] = dep[u] + 1, dfs(v);
  }
}
void solve() {
  for (int i = (1), iend = (m); i <= iend; ++i) {
    if (nxt[i] <= m) e[nxt[i]].push_back(i), deg[i]++;
  }
  for (int i = (1), iend = (m); i <= iend; ++i) {
    if (!deg[i]) dep[i] = 1, dfs(i);
  }
}
}  // namespace GETto
int main() {
  scanf("%d %d %d", &n, &m, &q);
  for (int i = (1), iend = (n); i <= iend; ++i)
    scanf("%d", p + i), mp[p[i]] = i;
  for (int i = (1), iend = (m); i <= iend; ++i) scanf("%d", a + i);
  fill(pos + 1, pos + n + 1, m + 1);
  for (int i = (m), iend = (1); i >= iend; --i) {
    nxt[i] = pos[p[mp[a[i]] % n + 1]];
    pos[a[i]] = i;
  }
  nxt[m + 1] = m + 1;
  GETto::solve();
  build();
  static int ans[maxn];
  for (int i = (1), iend = (q); i <= iend; ++i) {
    int l, r;
    scanf("%d %d", &l, &r);
    ans[i] = query(l, r) <= r;
  }
  for (int i = (1), iend = (q); i <= iend; ++i) putchar(ans[i] | 48);
  return 0;
}
