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;
template <typename T>
inline T read() {
  T x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = (x << 1) + (x << 3) + (ch ^ 48);
    ch = getchar();
  }
  return x * f;
}
const int N = 200010, INF = 0x3f3f3f3f;
int n, m, Q, p[N], a[N], id[N], last[N];
int lg2[N], nxt[N][21];
void init_lg() {
  for (int i = 2; i <= max(n, m); i++) lg2[i] = lg2[i >> 1] + 1;
}
void init() {
  for (int i = m; i >= 1; i--) {
    nxt[i][0] = last[p[id[a[i]] % n + 1]];
    last[a[i]] = i;
  }
  for (int i = 1; i <= lg2[n]; i++) {
    for (int j = 1; j <= m; j++) nxt[j][i] = nxt[nxt[j][i - 1]][i - 1];
  }
}
int minx[N][21];
void init_ST() {
  memset(minx, 0x3f, sizeof(minx));
  for (int i = 1; i <= m; i++) {
    int x = i;
    for (int j = 0; j <= lg2[n - 1]; j++) {
      if ((n - 1) >> j & 1) x = nxt[x][j];
    }
    minx[i][0] = x ? x : INF;
  }
  for (int i = 1; i <= lg2[m]; i++) {
    for (int j = 1; j <= m - (1 << i) + 1; j++) {
      minx[j][i] = min(minx[j][i - 1], minx[j + (1 << (i - 1))][i - 1]);
    }
  }
}
inline int query(int l, int r) {
  int k = lg2[r - l + 1];
  return min(minx[l][k], minx[r - (1 << k) + 1][k]);
}
int main() {
  n = read<int>(), m = read<int>(), Q = read<int>();
  init_lg();
  for (int i = 1; i <= n; i++) p[i] = read<int>(), id[p[i]] = i;
  for (int i = 1; i <= m; i++) a[i] = read<int>();
  init_lg();
  init();
  init_ST();
  while (Q--) {
    int l = read<int>(), r = read<int>();
    putchar(query(l, r) <= r ? '1' : '0');
  }
  puts("");
  return 0;
}
