You have an array of positive integers a[1], a[2], ..., a[n] and a set of bad prime numbers b1, b2, ..., bm. The prime numbers that do not occur in the set b are considered good. The beauty of array a is the sum <image>, where function f(s) is determined as follows:

  * f(1) = 0; 
  * Let's assume that p is the minimum prime divisor of s. If p is a good prime, then <image>, otherwise <image>. 



You are allowed to perform an arbitrary (probably zero) number of operations to improve array a. The operation of improvement is the following sequence of actions:

  * Choose some number r (1 ≤ r ≤ n) and calculate the value g = GCD(a[1], a[2], ..., a[r]). 
  * Apply the assignments: <image>, <image>, ..., <image>. 



What is the maximum beauty of the array you can get? 

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 5000) showing how many numbers are in the array and how many bad prime numbers there are.

The second line contains n space-separated integers a[1], a[2], ..., a[n] (1 ≤ a[i] ≤ 109) — array a. The third line contains m space-separated integers b1, b2, ..., bm (2 ≤ b1 < b2 < ... < bm ≤ 109) — the set of bad prime numbers.

Output

Print a single integer — the answer to the problem.

Examples

Input

5 2
4 20 34 10 10
2 5


Output

-2


Input

4 5
2 4 8 16
3 5 7 11 17


Output

10

Note

Note that the answer to the problem can be negative.

The GCD(x1, x2, ..., xk) is the maximum positive integer that divides each xi.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.HashSet;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.Map;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author prakharjain
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        _403B solver = new _403B();
        solver.solve(1, in, out);
        out.close();
    }

    static class _403B {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();

            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
            }

            HashSet<Integer> bs = new HashSet<>();

            int[] b = new int[m];
            for (int i = 0; i < m; i++) {
                b[i] = in.nextInt();
                bs.add(b[i]);
            }

            long ans = 0;

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

                int bc = 0;
                int gc = 0;

                for (int j = 2; j * j <= gcd; j++) {
                    if (gcd % j == 0) {
                        boolean isb = bs.contains(j);
                        while (gcd % j == 0) {
                            gcd /= j;
                            if (isb) {
                                bc++;
                            } else {
                                gc++;
                            }
                        }
                    }
                }

                if (gcd > 1) {
                    if (bs.contains(gcd)) {
                        bc++;
                    } else {
                        gc++;
                    }
                }

                ans -= bc;
                ans += gc;
            }

            int[] gcda = new int[n];

            gcda[0] = a[0];

            for (int i = 1; i < n; i++) {
                gcda[i] = gcd(gcda[i - 1], a[i]);
            }

            int td = 1;

            Map<Integer, Integer> pm = new HashMap<>();

            long bc = 0;
            long gc = 0;

            for (int i = n - 1; i >= 0; i--) {
                int gcd = gcda[i] / td;
                int ogcd = gcda[i];

                int cgcd = gcd;

                Map<Integer, Integer> cm = new HashMap<>();

                if (i == n - 1) {
                    for (int j = 2; j * j <= gcd; j++) {
                        if (gcd % j == 0) {
                            boolean isb = bs.contains(j);
                            while (gcd % j == 0) {
                                pm.merge(j, 1, (x, y) -> x + y);
                                gcd /= j;
                                if (isb) {
                                    bc++;
                                } else {
                                    gc++;
                                }
                            }
                        }
                    }

                    if (gcd > 1) {
                        pm.merge(gcd, 1, (x, y) -> x + y);
                        if (bs.contains(gcd)) {
                            bc++;
                        } else {
                            gc++;
                        }
                    }
                } else {
                    int num = ogcd / gcda[i + 1];

                    for (int j = 2; j * j <= num; j++) {
                        if (num % j == 0) {
                            boolean isb = bs.contains(j);
                            while (num % j == 0) {
                                pm.merge(j, 1, (x, y) -> x + y);
                                num /= j;
                                if (isb) {
                                    bc++;
                                } else {
                                    gc++;
                                }
                            }
                        }
                    }

                    if (num > 1) {
                        pm.merge(num, 1, (x, y) -> x + y);
                        if (bs.contains(num)) {
                            bc++;
                        } else {
                            gc++;
                        }
                    }
                }

                if (bc > gc) {
                    for (int j = 0; j <= i; j++) {
                        a[j] /= cgcd;
                    }
                    ans += (i + 1) * bc;
                    ans -= (i + 1) * gc;
                    td *= cgcd;
                    bc = 0;
                    gc = 0;
                    pm.clear();
                }
            }

            out.println(ans);


        }

        int gcd(int a, int b) {
            if (b == 0)
                return a;
            else
                return gcd(b, a % b);
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

