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;
inline int read() {
  int x = 0, f = 1;
  char c = getchar();
  while ((c < '0' || c > '9') && c != '-') c = getchar();
  if (c == '-') f = -1, c = getchar();
  while (c >= '0' && c <= '9') x = (x << 3) + (x << 1) + c - '0', c = getchar();
  return f * x;
}
int n, m, q, a[200001], b[200001], pre[200001], last[200001], pos[200001],
    k[800001], f[200001][20];
void build(int o, int l, int r) {
  if (l == r) {
    k[o] = pos[l];
    return;
  }
  int mid = (l + r) >> 1;
  build(o << 1, l, mid);
  build(o << 1 | 1, mid + 1, r);
  k[o] = max(k[o << 1], k[o << 1 | 1]);
}
int ask(int o, int l, int r, int x, int y) {
  if (l > y || x > r) return 0;
  if (x <= l && r <= y) return k[o];
  int mid = (l + r) >> 1;
  return max(ask(o << 1, l, mid, x, y), ask(o << 1 | 1, mid + 1, r, x, y));
}
int main() {
  n = read();
  m = read();
  q = read();
  for (register int i = 1; i <= n; ++i) a[i] = read();
  a[0] = a[n];
  for (register int i = 1; i <= n; ++i) pre[a[i]] = a[i - 1];
  for (register int i = 1; i <= m; ++i) b[i] = read();
  for (register int i = 1; i <= m; ++i) {
    f[i][0] = last[pre[b[i]]];
    last[b[i]] = i;
  }
  for (register int i = 1; i <= m; ++i)
    for (register int j = 1; j <= 18; j++) f[i][j] = f[f[i][j - 1]][j - 1];
  for (register int i = 1; i <= m; ++i) {
    pos[i] = i;
    for (register int j = 18; j >= 0; j--)
      if ((n - 1) & (1 << j)) pos[i] = f[pos[i]][j];
  }
  build(1, 1, m);
  while (q--) {
    int x = read();
    int y = read();
    if (ask(1, 1, m, x, y) >= x)
      printf("1");
    else
      printf("0");
  }
  printf("\n");
  return 0;
}
