Adilbek's house is located on a street which can be represented as the OX axis. This street is really dark, so Adilbek wants to install some post lamps to illuminate it. Street has n positions to install lamps, they correspond to the integer numbers from 0 to n - 1 on the OX axis. However, some positions are blocked and no post lamp can be placed there.

There are post lamps of different types which differ only by their power. When placed in position x, post lamp of power l illuminates the segment [x; x + l]. The power of each post lamp is always a positive integer number.

The post lamp shop provides an infinite amount of lamps of each type from power 1 to power k. Though each customer is only allowed to order post lamps of exactly one type. Post lamps of power l cost a_l each.

What is the minimal total cost of the post lamps of exactly one type Adilbek can buy to illuminate the entire segment [0; n] of the street? If some lamps illuminate any other segment of the street, Adilbek does not care, so, for example, he may place a lamp of power 3 in position n - 1 (even though its illumination zone doesn't completely belong to segment [0; n]).

Input

The first line contains three integer numbers n, m and k (1 ≤ k ≤ n ≤ 10^6, 0 ≤ m ≤ n) — the length of the segment of the street Adilbek wants to illuminate, the number of the blocked positions and the maximum power of the post lamp available.

The second line contains m integer numbers s_1, s_2, ..., s_m (0 ≤ s_1 < s_2 < ... s_m < n) — the blocked positions.

The third line contains k integer numbers a_1, a_2, ..., a_k (1 ≤ a_i ≤ 10^6) — the costs of the post lamps.

Output

Print the minimal total cost of the post lamps of exactly one type Adilbek can buy to illuminate the entire segment [0; n] of the street.

If illumintaing the entire segment [0; n] is impossible, print -1.

Examples

Input

6 2 3
1 3
1 2 3


Output

6


Input

4 3 4
1 2 3
1 10 100 1000


Output

1000


Input

5 1 5
0
3 3 3 3 3


Output

-1


Input

7 4 3
2 4 5 6
3 14 15


Output

-1

import java.io.*;
import java.nio.charset.Charset;

public class Contest45E {
    public static void main(String[] args) throws FileNotFoundException {
        boolean local = System.getProperty("ONLINE_JUDGE") == null;
        IOUtil io;
        if (local) {
            io = new IOUtil(new FileInputStream("E:\\DATABASE\\TESTCASE\\codeforces\\Contest45E.in"), new FileOutputStream("E:\\DATABASE\\TESTCASE\\codeforces\\Contest45E.out"));
        } else {
            io = new IOUtil(System.in, System.out);
        }

        Task task = new Task(io);
        task.run();
        io.flush();
    }

    public static class Task implements Runnable {
        IOUtil io;
        long INF = (long) 1e18;

        public Task(IOUtil io) {
            this.io = io;
        }

        @Override
        public void run() {
            int n = io.readInt();
            int m = io.readInt();
            int k = io.readInt();

            boolean[] blocked = new boolean[n + 1];
            int[] last = new int[n + 1];
            for (int i = 0; i < m; i++) {
                blocked[io.readInt()] = true;
            }

            int[] prices = new int[k + 1];
            for (int i = 1; i <= k; i++) {
                prices[i] = io.readInt();
            }

            last[0] = blocked[0] ? -1 : 0;
            for (int i = 1; i < n; i++) {
                last[i] = blocked[i] ? last[i - 1] : i;
            }

            long min = INF;
            for (int i = 1; i <= k; i++) {
                long total = 0;
                int next = 0;
                while (next < n) {
                    int choose = last[next];
                    if (choose < 0 || choose + i < next + 1) {
                        total = INF;
                        break;
                    }
                    next = choose + i;
                    total += prices[i];
                }

                min = Math.min(min, total);
            }

            if (min == INF) {
                io.write(-1);
                return;
            }
            io.write(min);
            return;
        }
    }

    public static class IOUtil {
        private static int BUF_SIZE = 1 << 13;

        private byte[] r_buf = new byte[BUF_SIZE];
        private int r_cur;
        private int r_total;
        private int r_next;
        private final InputStream in;
        private StringBuilder temporary = new StringBuilder();

        StringBuilder w_buf = new StringBuilder();
        private final OutputStream out;

        public IOUtil(InputStream in, OutputStream out) {
            this.in = in;
            this.out = out;
        }

        private void skipBlank() {
            while (r_next <= 32) {
                r_next = read();
            }
        }

        public int readString(char[] data, int offset, int limit) {
            skipBlank();

            int originalLimit = limit;
            while (limit > 0 && r_next > 32) {
                data[offset++] = (char) r_next;
                limit--;
                r_next = read();
            }

            return originalLimit - limit;
        }

        public String readString(StringBuilder builder) {
            skipBlank();

            while (r_next > 32) {
                builder.append((char) r_next);
                r_next = read();
            }

            return builder.toString();
        }

        public String readString() {
            temporary.setLength(0);
            return readString(temporary);
        }

        public long readUnsignedLong() {
            skipBlank();

            long num = 0;
            while (r_next >= '0' && r_next <= '9') {
                num = num * 10 + r_next - '0';
                r_next = read();
            }
            return num;
        }

        public long readLong() {
            skipBlank();

            int sign = 1;
            while (r_next == '+' || r_next == '-') {
                if (r_next == '-') {
                    sign *= -1;
                }
                r_next = read();
            }

            return sign == 1 ? readUnsignedLong() : readNegativeLong();
        }

        public long readNegativeLong() {
            skipBlank();

            long num = 0;
            while (r_next >= '0' && r_next <= '9') {
                num = num * 10 - r_next + '0';
                r_next = read();
            }
            return num;
        }

        public int readUnsignedInt() {
            skipBlank();

            int num = 0;
            while (r_next >= '0' && r_next <= '9') {
                num = num * 10 + r_next - '0';
                r_next = read();
            }
            return num;
        }

        public int readNegativeInt() {
            skipBlank();

            int num = 0;
            while (r_next >= '0' && r_next <= '9') {
                num = num * 10 - r_next + '0';
                r_next = read();
            }
            return num;
        }

        public int readInt() {
            skipBlank();

            int sign = 1;
            while (r_next == '+' || r_next == '-') {
                if (r_next == '-') {
                    sign *= -1;
                }
                r_next = read();
            }

            return sign == 1 ? readUnsignedInt() : readNegativeInt();
        }

        public int read() {
            while (r_total <= r_cur) {
                try {
                    r_total = in.read(r_buf);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                r_cur = 0;
                if (r_total == -1) {
                    return -1;
                }
            }
            return r_buf[r_cur++];
        }

        public void write(char c) {
            w_buf.append(c);
        }

        public void write(int n) {
            w_buf.append(n);
        }

        public void write(String s) {
            w_buf.append(s);
        }

        public void write(long s) {
            w_buf.append(s);
        }

        public void write(double s) {
            w_buf.append(s);
        }

        public void write(float s) {
            w_buf.append(s);
        }

        public void write(Object s) {
            w_buf.append(s);
        }

        public void write(char[] data, int offset, int cnt) {
            for (int i = offset, until = offset + cnt; i < until; i++) {
                write(data[i]);
            }
        }

        public void flush() {
            try {
                out.write(w_buf.toString().getBytes(Charset.forName("ascii")));
                w_buf.setLength(0);
                out.flush();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public double readDouble() {
            return Double.parseDouble(readString());
        }
    }
}
