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.
//Created by Aminul on 3/31/2019.

import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.Scanner;
import static java.lang.Math.min;

public class E_ {
    public static void main(String[] args) throws Exception {
        Scanner in = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n = in.nextInt(), m = in.nextInt(), q = in.nextInt();
        int p[] = new int[n + 1], map[] = new int[n + 1], a[] = new int[m + 1];
        ArrayDeque<Integer> dq[] = genDQ(n + 1), g[] = genDQ(m + 1);
        for (int i = 1; i <= n; i++) {
            p[i] = in.nextInt();
            map[p[i]] = i;
        }
        for (int i = 1; i <= m; i++) {
            a[i] = in.nextInt();
            a[i] = map[a[i]];
            dq[a[i]].addLast(i);
            int prev = a[i] - 1;
            if (prev == 0) prev = n;
            while (!dq[prev].isEmpty()) {
                int u = dq[prev].pollLast();
                g[i].addLast(u);
            }
        }
        int pos[] = new int[m + 1], vis[] = new int[m + 1], arr[] = new int[m + 1];
        Arrays.fill(pos, (int) 1e9);
        for (int i = m; i >= 1; i--) {
            if (vis[i] == 0) dfs(i, 1, n, vis, arr, pos, g);
        }
        SparseTable RMQ = new SparseTable(pos);
        for (int i = 1; i <= q; i++) {
            int l = in.nextInt(), r = in.nextInt();
            if (RMQ.query(l, r) <= r) pw.print("1");
            else pw.print("0");
        }
        pw.println();

        pw.close();
    }

    static void dfs(int u, int id, int n, int vis[], int arr[], int pos[], ArrayDeque<Integer> g[]) {
        vis[u] = 1;
        arr[id] = u;
        if (id >= n) pos[u] = arr[id - n + 1];
        for (int v : g[u]) {
            if (vis[v] == 0) {
                dfs(v, id + 1, n, vis, arr, pos, g);
            }
        }
    }

    static <T> ArrayDeque<T>[] genDQ(int n) {
        ArrayDeque<T> list[] = new ArrayDeque[n];
        for (int i = 0; i < n; i++) list[i] = new ArrayDeque<T>();
        return list;
    }

    static void debug(Object... obj) {
        System.err.println(Arrays.deepToString(obj));
    }

    static class SparseTable {
        int[] logTable;
        int[][] rmq;
        int[] a;

        public SparseTable(int[] a) {
            this.a = a;
            int n = a.length;

            logTable = new int[n + 1];
            for (int i = 2; i <= n; i++)
                logTable[i] = logTable[i >> 1] + 1;

            rmq = new int[logTable[n] + 1][n];

            for (int i = 0; i < n; ++i)
                rmq[0][i] = a[i];

            for (int k = 1; (1 << k) < n; ++k) {
                for (int i = 0; i + (1 << k) <= n; i++) {
                    int x = rmq[k - 1][i];
                    int y = rmq[k - 1][i + (1 << k - 1)];
                    rmq[k][i] = min(x, y); // change here for other type of queries, ie : max, gcd, and, or etc
                }
            }
        }

        public int query(int i, int j) {
            int k = logTable[j - i];
            int x = rmq[k][i];
            int y = rmq[k][j - (1 << k) + 1];
            return min(x, y); // change here for other type of queries, ie : max, gcd, and, or etc
        }
    }
}