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 n, m, que, a[400005], b[400005], pos[400005], t, las[400005], f[400005][22],
    g[400005], a1, a2, ans;
struct node {
  int l, r, v;
  node *ch[2];
} * root;
int gets() {
  int v = 0;
  char ch;
  bool f = 0;
  while (!isdigit(ch = getchar()))
    if (ch == '-') f = 1;
  v = ch - 48;
  while (isdigit(ch = getchar())) v = (v << 1) + (v << 3) + ch - 48;
  return f ? -v : v;
}
void pushup(node *x) { x->v = max(x->ch[0]->v, x->ch[1]->v); }
void build(node *&x, int l, int r) {
  x = new node();
  x->l = l, x->r = r;
  if (l == r) {
    x->v = g[l];
    return;
  }
  int mid = l + r >> 1;
  build(x->ch[0], l, mid);
  build(x->ch[1], mid + 1, r);
  pushup(x);
}
void ask(node *x, int l, int r) {
  if (x->l == l && x->r == r) {
    ans = max(ans, x->v);
    return;
  }
  int mid = x->l + x->r >> 1;
  if (r <= mid)
    ask(x->ch[0], l, r);
  else if (l > mid)
    ask(x->ch[1], l, r);
  else
    ask(x->ch[0], l, mid), ask(x->ch[1], mid + 1, r);
}
int main() {
  n = gets(), m = gets(), que = gets();
  for (int i = 1; i <= n; i++) a[i] = a[i + n] = gets(), pos[a[i]] = i + n;
  for (int i = 1; i <= m; i++) b[i] = gets();
  for (int i = 1; i <= m; i++) {
    t = a[pos[b[i]] - 1];
    f[i][0] = las[t];
    las[b[i]] = i;
  }
  for (int j = 1; j <= 20; j++)
    for (int i = 1; i <= m; i++) f[i][j] = f[f[i][j - 1]][j - 1];
  for (int i = 1; i <= m; i++) {
    t = n - 1;
    g[i] = i;
    for (int j = 20; j >= 0; j--) {
      if (t & (1 << j)) g[i] = f[g[i]][j];
    }
  }
  build(root, 1, m);
  for (int i = 1; i <= que; i++) {
    a1 = gets(), a2 = gets();
    ans = 0;
    ask(root, a1, a2);
    if (a1 <= ans)
      printf("1");
    else
      printf("0");
  }
  puts("");
  return 0;
}
