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.OutputStream;
import java.util.Arrays;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            BLynyrdSkynyrd solver = new BLynyrdSkynyrd();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class BLynyrdSkynyrd {
        int[][] jump;
        int m;

        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            m = in.readInt();
            int q = in.readInt();
            int[] a = new int[n];
            int[] invA = new int[n + 1];
            for (int i = 0; i < n; i++) {
                a[i] = in.readInt();
                invA[a[i]] = i;
            }
            int[] b = new int[m];
            for (int i = 0; i < m; i++) {
                b[i] = invA[in.readInt()];
            }

            jump = new int[m][20];
            SequenceUtils.deepFill(jump, m);
            int[] registry = new int[n];
            SequenceUtils.deepFill(registry, m);
            for (int i = m - 1; i >= 0; i--) {
                int next = (b[i] + 1) % n;
                jump[i][0] = registry[next];
                registry[b[i]] = i;
                for (int j = 0; jump[i][j] != m; j++) {
                    jump[i][j + 1] = jump[jump[i][j]][j];
                }
            }

            int[] right = new int[m];
            for (int i = 0; i < m; i++) {
                right[i] = jump(i, n - 1);
            }

            IntegerSparseTable st = new IntegerSparseTable(right, m, (x, y) -> Math.min(x, y));
            for (int i = 0; i < q; i++) {
                int l = in.readInt() - 1;
                int r = in.readInt() - 1;
                int min = st.query(l, r);
                out.append(min <= r ? '1' : '0');
            }
        }

        public int jump(int i, int k) {
            if (i == m) {
                return i;
            }
            if (k == 0) {
                return i;
            }
            int log = CachedLog2.floorLog(k);
            return jump(jump[i][log], k - (1 << log));
        }

    }

    static class SequenceUtils {
        public static void deepFill(Object array, int val) {
            if (!array.getClass().isArray()) {
                throw new IllegalArgumentException();
            }
            if (array instanceof int[]) {
                int[] intArray = (int[]) array;
                Arrays.fill(intArray, val);
            } else {
                Object[] objArray = (Object[]) array;
                for (Object obj : objArray) {
                    deepFill(obj, val);
                }
            }
        }

    }

    static class CachedLog2 {
        private static final int BITS = 16;
        private static final int LIMIT = 1 << BITS;
        private static final byte[] CACHE = new byte[LIMIT];

        static {
            int b = 0;
            for (int i = 0; i < LIMIT; i++) {
                while ((1 << (b + 1)) <= i) {
                    b++;
                }
                CACHE[i] = (byte) b;
            }
        }

        public static int floorLog(int x) {
            return x < LIMIT ? CACHE[x] : (BITS + CACHE[x >>> BITS]);
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 20];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class IntegerSparseTable {
        private int[][] st;
        private IntegerBinaryFunction merger;

        public IntegerSparseTable(int[] data, int length, IntegerBinaryFunction merger) {
            int m = CachedLog2.floorLog(length);
            st = new int[m + 1][length];
            this.merger = merger;
            for (int i = 0; i < length; i++) {
                st[0][i] = data[i];
            }
            for (int i = 0; i < m; i++) {
                int interval = 1 << i;
                for (int j = 0; j < length; j++) {
                    if (j + interval < length) {
                        st[i + 1][j] = merge(st[i][j], st[i][j + interval]);
                    } else {
                        st[i + 1][j] = st[i][j];
                    }
                }
            }
        }

        private int merge(int a, int b) {
            return merger.apply(a, b);
        }

        public int query(int left, int right) {
            int queryLen = right - left + 1;
            int bit = CachedLog2.floorLog(queryLen);
            // x + 2^bit == right + 1
            // So x should be right + 1 - 2^bit - left=queryLen - 2^bit
            return merge(st[bit][left], st[bit][right + 1 - (1 << bit)]);
        }

        public String toString() {
            return Arrays.toString(st[0]);
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static interface IntegerBinaryFunction {
        int apply(int a, int b);

    }
}

