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;
const int NMAX = 2e5;
const int LG = 18;
int N, M, Q;
int prm[NMAX + 5], v[NMAX + 5];
int nxt[NMAX + 5], lst[NMAX + 5], nxtpos[LG + 2][NMAX + 5];
int rgt[NMAX + 5];
int lg2[NMAX + 5];
int rmq[LG + 2][NMAX + 5];
int main() {
  scanf("%d%d%d", &N, &M, &Q);
  for (int i = 1; i <= N; i++) {
    scanf("%d", &prm[i]);
    if (i > 1) nxt[prm[i - 1]] = prm[i];
  }
  nxt[prm[N]] = prm[1];
  for (int i = 1; i <= M; i++) scanf("%d", &v[i]);
  for (int i = 1; i <= N; i++) lst[i] = M + 1;
  nxtpos[0][M + 1] = M + 1;
  for (int i = M; i >= 1; i--) {
    nxtpos[0][i] = lst[nxt[v[i]]];
    lst[v[i]] = i;
  }
  for (int i = 1; (1 << i) <= N; i++)
    for (int j = 1; j <= M + 1; j++)
      nxtpos[i][j] = nxtpos[i - 1][nxtpos[i - 1][j]];
  for (int i = 1; i <= M; i++) {
    int pos = i;
    int rem = N - 1;
    for (int j = 0; (1 << j) <= rem; j++)
      if ((rem >> j) & 1) pos = nxtpos[j][pos];
    rgt[i] = pos;
    rmq[0][i] = rgt[i];
  }
  for (int i = 2; i <= M; i++) lg2[i] = lg2[i >> 1] + 1;
  for (int i = 1; (1 << i) <= M; i++)
    for (int j = 1; j + (1 << i) - 1 <= M; j++)
      rmq[i][j] = min(rmq[i - 1][j], rmq[i - 1][j + (1 << (i - 1))]);
  for (int q = 1; q <= Q; q++) {
    int st, dr;
    scanf("%d%d", &st, &dr);
    int lg = lg2[dr - st + 1];
    int pos = min(rmq[lg][st], rmq[lg][dr - (1 << lg) + 1]);
    printf("%d", (pos <= dr));
  }
  return 0;
}
