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 maxn = 2e5 + 5;
int pos[maxn], p[maxn];
int nxt[maxn], head[maxn], a[maxn];
int l[maxn];
int n, m, q;
int tree[maxn << 2];
int rmq[maxn][30];
void build(int L, int R, int k) {
  if (L == R) {
    tree[k] = l[L];
    return;
  }
  int mid = L + R >> 1;
  build(L, mid, k * 2);
  build(mid + 1, R, k * 2 + 1);
  tree[k] = min(tree[k * 2], tree[k * 2 + 1]);
}
const int INF = 1e9 + 5;
int query(int l1, int r1, int L, int R, int k) {
  if (l1 > R || L > r1) return INF;
  if (l1 <= L && r1 >= R) return tree[k];
  int mid = L + R >> 1;
  return min(query(l1, r1, L, mid, k * 2),
             query(l1, r1, mid + 1, R, k * 2 + 1));
}
int main() {
  cin >> n >> m >> q;
  for (int i = 1; i <= n; i++) {
    cin >> p[i];
    pos[p[i]] = i;
    head[i] = m + 1;
  }
  for (int i = 1; i <= m; i++) cin >> a[i];
  for (int i = m; i >= 1; i--) {
    int q = pos[a[i]] + 1;
    if (q == n + 1) q = 1;
    nxt[i] = head[p[q]];
    rmq[i][0] = nxt[i];
    head[a[i]] = i;
  }
  for (int i = 1; i <= 24; i++)
    for (int j = 1; j <= m; j++)
      if (rmq[j][i - 1] > m)
        rmq[j][i] = m + 1;
      else
        rmq[j][i] = rmq[rmq[j][i - 1]][i - 1];
  for (int i = 1; i <= m; i++) {
    int d = i, p = n;
    for (int j = 24; j >= 0; j--) {
      if (d > m) break;
      if ((1 << j) < p) {
        p -= 1 << j;
        d = rmq[d][j];
      }
    }
    l[i] = d;
  }
  build(1, m, 1);
  int L, R;
  while (q--) {
    cin >> L >> R;
    int d = query(L, R, 1, m, 1);
    if (d <= R)
      cout << 1;
    else
      cout << 0;
  }
}
