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 abs(T zz) {
  return zz < 0 ? -zz : zz;
}
template <typename T>
inline T sqr(T zz) {
  return zz * zz;
}
const int N = 200500;
const int L = 20;
int n, m, q;
int a[N];
int p[N], rp[N];
int pos[N];
int nx[L][N];
int dp[N];
int tr[4 * N];
void build(int idx, int lf, int rg) {
  if (lf == rg) {
    tr[idx] = dp[lf];
  } else {
    int mid = (lf + rg) / 2;
    build(2 * idx + 1, lf, mid);
    build(2 * idx + 2, mid + 1, rg);
    tr[idx] = min(tr[2 * idx + 1], tr[2 * idx + 2]);
  }
}
int get_min(int qlf, int qrg, int idx, int lf, int rg) {
  if (qlf == lf && qrg == rg) {
    return tr[idx];
  } else {
    int mid = (lf + rg) / 2;
    int ans = N;
    if (qlf <= mid) {
      ans = min(ans, get_min(qlf, min(mid, qrg), 2 * idx + 1, lf, mid));
    }
    if (mid + 1 <= qrg) {
      ans = min(ans, get_min(max(mid + 1, qlf), qrg, 2 * idx + 2, mid + 1, rg));
    }
    return ans;
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cin >> n >> m >> q;
  for (int i = (0); i < (n); ++i) {
    cin >> p[i];
    p[i]--;
    rp[p[i]] = i;
  }
  for (int i = (0); i < (m); ++i) {
    cin >> a[i];
    a[i]--;
  }
  {
    memset(pos, -1, sizeof(pos));
    for (int i = m - 1; i >= 0; --i) {
      nx[0][i] = pos[p[(rp[a[i]] + 1) % n]];
      pos[a[i]] = i;
    }
    for (int i = 1; i < L; ++i) {
      for (int j = 0; j < m; ++j) {
        if (nx[i - 1][j] == -1) {
          nx[i][j] = -1;
        } else {
          nx[i][j] = nx[i - 1][nx[i - 1][j]];
        }
      }
    }
  }
  for (int i = (0); i < (m); ++i) {
    int pos = i;
    int left = n - 1;
    for (int j = L - 1; j >= 0; j--) {
      if ((1 << j) <= left) {
        pos = nx[j][pos];
        left -= (1 << j);
        if (pos == -1) {
          break;
        }
      }
    }
    if (pos == -1) {
      dp[i] = N;
    } else {
      dp[i] = pos;
    }
  }
  build(0, 0, m - 1);
  string ans;
  ans.reserve(q);
  for (int i = (0); i < (q); ++i) {
    int lf, rg;
    cin >> lf >> rg;
    lf--;
    rg--;
    int dp_min = get_min(lf, rg, 0, 0, m - 1);
    if (dp_min <= rg) {
      ans.push_back('1');
    } else {
      ans.push_back('0');
    }
  }
  cout << ans << endl;
  return 0;
}
