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;
namespace mine {
const int INF = 0x3f3f3f3f;
const long long LLINF = 0x3f3f3f3f3f3f3f3fll;
long long qread() {
  long long ans = 0;
  char c = getchar();
  int f = 1;
  while (c < '0' or c > '9') {
    if (c == '-') f = -1;
    c = getchar();
  }
  while ('0' <= c and c <= '9') ans = ans * 10 + c - '0', c = getchar();
  return ans * f;
}
void write(long long num) {
  if (num < 0) {
    num = -num;
    putchar('-');
  }
  if (num > 9) write(num / 10);
  putchar('0' + num % 10);
}
void write1(long long num) {
  write(num);
  putchar(' ');
}
void write2(long long num) {
  write(num);
  puts("");
}
void chmax(long long &x, const long long y) { x = x > y ? x : y; }
void chmin(long long &x, const long long y) { x = x < y ? x : y; }
const int MAX_N = 2e5 + 10;
const long long MOD = 1e9 + 7;
void add(long long &x, long long y) {
  x += y;
  if (x >= MOD) x -= MOD;
  if (x < 0) x += MOD;
}
int a[MAX_N], num[MAX_N];
int lst[MAX_N], nxt2[MAX_N];
int bin[30], mm[MAX_N][20], nxt[MAX_N][20];
int jump(int x, int k) {
  for (int t = 19; t >= 0; t--)
    if (k & bin[t]) x = nxt[x][t];
  return x;
}
void main() {
  bin[0] = 1;
  for (int i = 1; i < 30; i++) bin[i] = bin[i - 1] << 1;
  int n = qread(), m = qread(), q = qread();
  for (int i = 1; i <= n; i++) a[qread()] = i;
  for (int i = 1; i <= m; i++) num[i] = a[qread()];
  for (int i = 1; i <= n + 1; i++) lst[i] = m + 1;
  nxt[m + 1][0] = m + 1;
  for (int i = m; i >= 1; i--) {
    lst[num[i]] = i, nxt[i][0] = lst[num[i] + 1];
    if (num[i] == n) nxt2[i] = lst[1];
  }
  for (int t = 1; t < 20; t++)
    for (int i = 1; i <= m + 1; i++) nxt[i][t] = nxt[nxt[i][t - 1]][t - 1];
  for (int i = 1; i <= m; i++) {
    int to = jump(i, n - num[i]);
    if (num[i] == 1)
      mm[i][0] = to;
    else if (nxt2[to])
      mm[i][0] = jump(nxt2[to], num[i] - 2);
    else
      mm[i][0] = INF;
  }
  for (int t = 1; t < 20; t++)
    for (int i = 1; i <= m - bin[t] + 1; i++)
      mm[i][t] = min(mm[i][t - 1], mm[i + bin[t - 1]][t - 1]);
  while (q--) {
    int l = qread(), r = qread();
    int t = log2(r - l + 1), ans = min(mm[l][t], mm[r - bin[t] + 1][t]);
    write(ans <= r);
  }
}
};  // namespace mine
int main() {
  srand(time(0));
  mine::main();
}
