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 Linf = 0x7f7f7f7f7f7f7f7f;
const int Inf = 0x3f3f3f3f;
char buf[100000], *p1 = buf, *p2 = buf;
const int MAXN = 2e5 + 10;
inline char nc() {
  return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 100000, stdin), p1 == p2)
             ? EOF
             : *p1++;
}
inline int read() {
  int w = 1, data = 0;
  char ch = 0;
  while (ch != '-' && (ch < '0' || ch > '9')) ch = nc();
  if (ch == '-') w = -1, ch = nc();
  while (ch >= '0' && ch <= '9') data = data * 10 + ch - '0', ch = nc();
  return w * data;
}
int n, m, q, que[MAXN];
int fa[MAXN][20], a[MAXN], b[MAXN], id[MAXN], lst[MAXN];
int query(int x) {
  for (int i = 25; i >= 0; i--)
    if ((n - 1) & (1 << i)) x = fa[x][i];
  return x;
}
int main() {
  n = read(), m = read(), q = read();
  for (int i = 1; i <= n; i++) a[i] = read(), id[a[i]] = i;
  a[0] = a[n];
  memset(que, 0x3f, sizeof que);
  for (int i = 1; i <= m; i++) {
    b[i] = read();
    if (id[b[i]] == 1)
      fa[i][0] = lst[n];
    else
      fa[i][0] = lst[id[b[i]] - 1];
    lst[id[b[i]]] = i;
  }
  int lg = log(max(n, m)) / log(2) + 1;
  for (int j = 1; j <= lg; j++)
    for (int i = 1; i <= m; i++) fa[i][j] = fa[fa[i][j - 1]][j - 1];
  for (int i = m, l; i >= 1; i--) {
    l = query(i);
    if (l == 0) continue;
    que[l] = min(que[l], i);
  }
  for (int i = m, r = Inf; i >= 1; i--)
    r = min(r, que[i]), que[i] = min(que[i], r);
  for (int i = 1; i <= q; i++) {
    int l = read(), r = read();
    if (que[l] <= r)
      cout << '1';
    else
      cout << '0';
  }
  return 0;
}
