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;
int p[200050], q[200050], b[200050], go[200050][18], dp[200050][18];
inline void read(int&);
inline int query(int, int), query1(int, int), flog2(float);
int main() {
  int n, m, qq;
  read(n), read(m), read(qq);
  for (int i(1); i <= n; ++i) read(p[i]), q[p[i]] = i;
  for (int i(1), x; i <= m; ++i) {
    read(x), b[x] = i;
    go[i][0] = b[p[(q[x] - 2 + n) % n + 1]];
  }
  for (int i, j(1); j < 18; ++j)
    for (i = 1; i <= m; ++i) go[i][j] = go[go[i][j - 1]][j - 1];
  for (int i(1); i <= m; ++i) dp[i][0] = query(i, n - 1);
  for (int i, j(1); j < 18; ++j)
    for (i = 1; i + (1 << j) - 1 <= m; ++i)
      dp[i][j] = max(dp[i][j - 1], dp[i + (1 << j - 1)][j - 1]);
  for (int i(1), l, r; i <= qq; ++i)
    read(l), read(r), putchar(query1(l, r) >= l ? 49 : 48);
  return 0;
}
inline int flog2(float x) { return ((unsigned&)x >> 23) - 127; }
inline int query1(int l, int r) {
  int len(flog2(r - l + 1));
  return max(dp[l][len], dp[r - (1 << len) + 1][len]);
}
inline int query(int p, int n) {
  for (int i(17); ~i; --i)
    if (n >> i & 1) p = go[p][i];
  return p;
}
inline void read(int& x) {
  x ^= x;
  register char c;
  while (c = getchar(), c < '0' || c > '9')
    ;
  while (c >= '0' && c <= '9')
    x = (x << 1) + (x << 3) + (c ^ 48), c = getchar();
}
