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 <class T>
inline T lowbit(T x) {
  return x & (-x);
}
template <class T>
T gcd(T a, T b) {
  return b ? gcd(b, a % b) : a;
}
template <class T>
inline T Pow(T a, T b, T p) {
  T ret = 1;
  a %= p;
  for (; b; b >>= 1, a = a * a % p)
    if (b & 1) (ret *= a) %= p;
  return ret;
}
template <class T>
inline void read(T &ret) {
  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 * 10 + ch - '0';
    ch = getchar();
  }
  ret = x * f;
}
const int N = 2e5 + 10, lgN = 20;
int lg2[N];
struct ST {
  int st[N][lgN];
  void init(int *w, int n) {
    for (int i = (1); i <= (n); i++) st[i][0] = w[i];
    int lgn = ceil(log2(n));
    for (int j = (1); j <= (lgn); j++)
      for (int i = (1); i <= (n); i++) {
        st[i][j] = st[i][j - 1];
        int k = i + (1 << (j - 1));
        if (k < n) st[i][j] = min(st[i][j], st[k][j - 1]);
      }
  }
  long long query(int l, int r) {
    int len = r - l + 1, t = lg2[len];
    return min(st[l][t], st[r - (1 << t) + 1][t]);
  }
} rmq;
int n, m, q, lgn, p[N], loc[N], a[N];
int lst[N], nxt[N][lgN], w[N];
void init() {
  fill(lst, lst + n, m + 1);
  for (int i = (m); i >= (1); i--) {
    int tmp = p[(loc[a[i]] + 1) % n];
    nxt[i][0] = lst[tmp];
    lst[a[i]] = i;
  }
  lgn = ceil(log2(n));
  for (int i = (1); i <= (lgn); i++)
    for (int j = (1); j <= (m); j++) nxt[j][i] = nxt[nxt[j][i - 1]][i - 1];
}
int main() {
  read(n);
  read(m);
  read(q);
  for (int i = (0); i <= (n - 1); i++) read(p[i]), loc[p[i]] = i;
  for (int i = (1); i <= (m); i++) read(a[i]);
  init();
  for (int i = (1); i <= (m); i++) {
    w[i] = i;
    for (int j = (lgn); j >= (0); j--)
      if ((1 << j) & (n - 1)) w[i] = nxt[w[i]][j];
    if (w[i] == 0) w[i] = m + 1;
  }
  for (int i = 0; (1 << i) <= max(n, m); i++) lg2[1 << i] = i;
  for (int i = (1); i <= (max(n, m)); i++) lg2[i] = max(lg2[i], lg2[i - 1]);
  rmq.init(w, m);
  for (int i = (1); i <= (q); i++) {
    int l, r;
    read(l);
    read(r);
    printf(rmq.query(l, r) <= r ? "1" : "0");
  }
}
