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.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.io.InputStream;

/**
 * @author khokharnikunj8
 */

public class Main {
    public static void main(String[] args) {
        new Thread(null, new Runnable() {
            public void run() {
                new Main().solve();
            }
        }, "1", 1 << 26).start();
    }

    void solve() {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BLynyrdSkynyrd solver = new BLynyrdSkynyrd();
        solver.solve(1, in, out);
        out.close();
    }

    static class BLynyrdSkynyrd {
        int[][] last;

        public void solve(int testNumber, ScanReader in, PrintWriter out) {
            int n = in.scanInt();
            int m = in.scanInt();
            int q = in.scanInt();
            int[] permutation = new int[n];
            for (int i = 0; i < n; i++) permutation[i] = in.scanInt() - 1;
            int[] ar = new int[m];
            for (int i = 0; i < m; i++) ar[i] = in.scanInt() - 1;
            int[] prev = new int[n];
            prev[permutation[0]] = permutation[n - 1];
            for (int i = 0; i < n - 1; i++) prev[permutation[i + 1]] = permutation[i];

            last = new int[m][20];
            for (int i = 0; i < m; i++) Arrays.fill(last[i], -1);
            int pos[] = new int[n];
            Arrays.fill(pos, -1);
            for (int i = 0; i < m; i++) {
                pos[ar[i]] = i;
                last[i][0] = pos[prev[ar[i]]];
            }

            for (int j = 1; j < 20; j++) {
                for (int i = 0; i < m; i++) {
                    if (last[i][j - 1] != -1)
                        last[i][j] = last[last[i][j - 1]][j - 1];
                }
            }

            int LOL = n - 1;
            int anss[] = new int[m];
            for (int i = 0; i < m; i++) {
                int current = i;
                for (int j = 19; j >= 0 && current != -1; j--) {
                    if ((LOL & (1 << j)) != 0)
                        current = last[current][j];
                }
                anss[i] = current;
                //  out.println(anss[i]);
            }
            int[] temp = new int[m + 1];
            for (int i = 1; i <= m; i++) temp[i] = anss[i - 1];
            SegmentTreeMax seg = new SegmentTreeMax(temp, m);
            int queries[][] = new int[q][2];
            for (int i = 0; i < q; i++) {
                queries[i][0] = in.scanInt();
                queries[i][1] = in.scanInt();
                int query = seg.query(queries[i][0], queries[i][1]);
                //  out.print((query + 1) + " ");
                if (query + 1 >= queries[i][0] && query + 1 <= queries[i][1]) out.print(1);
                else out.print(0);
                //  out.println();


            }

        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int index;
        private BufferedInputStream in;
        private int total;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (index >= total) {
                index = 0;
                try {
                    total = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (total <= 0) return -1;
            }
            return buf[index++];
        }

        public int scanInt() {
            int integer = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                }
            }
            return neg * integer;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }

    static class SegmentTreeMax {
        int n;
        int[] t;
        int[] data;

        public SegmentTreeMax(int[] data, int n) {
            this.data = data;
            this.n = n;
            this.t = new int[2 * (n + 2)];
            build();
        }

        void build() {
            for (int i = 0; i < n; i++) t[i + n] = (data[i + 1] == 1000000001 ? -1 : data[i + 1]);
            for (int i = n - 1; i > 0; --i) t[i] = Math.max(t[i << 1], t[i << 1 | 1]);
        }

        public int query(int l, int r) {
            int res = -1;
            for (l += n - 1, r += n; l < r; l >>= 1, r >>= 1) {
                if ((l & 1) != 0) res = Math.max(res, t[l++]);
                if ((r & 1) != 0) res = Math.max(res, t[--r]);
            }
            return res;
        }

    }
}

