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>
template <typename T, typename _T>
inline bool chk_min(T &x, const _T y) {
  return y < x ? x = y, 1 : 0;
}
template <typename T, typename _T>
inline bool chk_max(T &x, const _T y) {
  return x < y ? x = y, 1 : 0;
}
const int N = (int)2e5 + 5;
int R[N][20], Mi[N][20], bin[(1 << 18) + 5], occ[N];
int a[N], pos[N], p[N];
int n, m, q;
int nxt(int x) {
  if (x == n)
    return 1;
  else
    return x + 1;
}
int jmp(int x, int k) {
  for (int i = (0), iEND = (18); i <= iEND; ++i)
    if ((1 << i) & k) {
      x = R[x][i];
      if (x == 1e9) return 1e9;
    }
  return x;
}
int query(int l, int r) {
  int k = bin[r - l + 1];
  return std::min(Mi[l][k], Mi[r - (1 << k) + 1][k]);
}
int main() {
  for (int i = (2), iEND = (1 << 18); i <= iEND; ++i) bin[i] = bin[i >> 1] + 1;
  scanf("%d%d%d", &n, &m, &q);
  for (int i = (1), iEND = (n); i <= iEND; ++i) scanf("%d", &p[i]);
  for (int i = (1), iEND = (m); i <= iEND; ++i) scanf("%d", &a[i]);
  for (int i = (1), iEND = (n); i <= iEND; ++i) pos[p[i]] = i;
  for (int i = (1), iEND = (m); i <= iEND; ++i) a[i] = pos[a[i]];
  for (int i = (1), iEND = (n); i <= iEND; ++i) occ[i] = 1e9;
  for (int i = (m), iEND = (1); i >= iEND; --i) {
    R[i][0] = occ[nxt(a[i])];
    occ[a[i]] = i;
  }
  for (int j = (1), jEND = (18); j <= jEND; ++j)
    for (int i = (1), iEND = (m); i <= iEND; ++i) {
      if (R[i][j - 1] == 1e9)
        R[i][j] = 1e9;
      else
        R[i][j] = R[R[i][j - 1]][j - 1];
    }
  for (int i = (1), iEND = (m); i <= iEND; ++i) Mi[i][0] = jmp(i, n - 1);
  for (int j = (1), jEND = (18); j <= jEND; ++j)
    for (int i = (1), iEND = (m - (1 << j) + 1); i <= iEND; ++i)
      Mi[i][j] = std::min(Mi[i][j - 1], Mi[i + (1 << (j - 1))][j - 1]);
  while (q--) {
    int l, r;
    scanf("%d%d", &l, &r);
    printf("%d", query(l, r) <= r);
  }
  puts("");
  return 0;
}
