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.*;
import java.math.*;
import java.util.*;
import java.lang.*;

public class Main implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

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

        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 String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        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 long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long 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 double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

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

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

    static long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

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

    static long modPow(long a, long p, long m) {
        if (a == 1) return 1;
        long ans = 1;
        while (p > 0) {
            if (p % 2 == 1) ans = (ans * a) % m;
            a = (a * a) % m;
            p >>= 1;
        }
        return ans;
    }

    static long modInv(long a, long m) {
        return modPow(a, m - 2, m);
    }


    static class Radix {


        static int getMax(int arr[], int n)
        {
            int mx = arr[0];
            for (int i = 1; i < n; i++)
                if (arr[i] > mx)
                    mx = arr[i];
            return mx;
        }

        static void countSort(int arr[], int n, int exp)
        {
            int output[] = new int[n];
            int i;
            int count[] = new int[10];
            Arrays.fill(count,0);

            for (i = 0; i < n; i++)
                count[ (arr[i]/exp)%10 ]++;

            for (i = 1; i < 10; i++)
                count[i] += count[i - 1];

            for (i = n - 1; i >= 0; i--)
            {
                output[count[ (arr[i]/exp)%10 ] - 1] = arr[i];
                count[ (arr[i]/exp)%10 ]--;
            }

            for (i = 0; i < n; i++)
                arr[i] = output[i];
        }

        static void radixsort(int arr[], int n)
        {
            int m = getMax(arr, n);

            for (int exp = 1; m/exp > 0; exp *= 10)
                countSort(arr, n, exp);
        }

    }

    class DSU{
        int par[],size[],connectedComponent;
        DSU(int n){
            par=new int[n];
            size=new int[n];
            for (int i = 0; i <n ; i++) {
                size[i]=1;
                par[i]=i;
            }
            connectedComponent=n;
        }
        int root(int n){
            if(n==par[n])return n;
            return par[n]=root(par[n]);
        }
        boolean union(int u,int v){
            return f_union(root(u),root(v));
        }
        boolean f_union(int u,int v){
            if(u==v)return false;
            if(size[u]>size[v]){
                size[u]+=size[v];
                par[v]=u;
            }
            else{
                size[v]+=size[u];
                par[u]=v;
            }
            connectedComponent--;
            return true;
        }
        DSU clone_DSU(){
            DSU t=new DSU(par.length);
            t.connectedComponent=connectedComponent;
            for (int i = 0; i <par.length ; i++) {
                t.par[i]=par[i];
                t.size[i]=size[i];
            }
            return t;
        }
    }

    int f(int n,ArrayList<Integer> l,HashSet<Integer> h){
        int ans=0;
        for(int x:l){
            while (n%x==0){
                n/=x;
                if(h.contains(x))ans--;
                else ans++;
            }
        }
        if(n!=1){
            if(h.contains(n))ans--;
            else ans++;
        }
        return ans;
    }


    public void run() {
        InputReader sc = new InputReader(System.in);
        //Scanner sc=new Scanner(System.in);
       // Random sc=new Random();
        PrintWriter out = new PrintWriter(System.out);

        int n=sc.nextInt();
        int m=sc.nextInt();
        int a[]=new int[n];
        int gcd=0;
        int preGCD[]=new int[n];
        for (int i = 0; i <n ; i++) {
            a[i]=sc.nextInt();
            gcd=gcd(gcd,a[i]);
            preGCD[i]=gcd;
        }

        int seive[]=new int[100000];
        seive[0]=seive[1]=1;
        ArrayList<Integer> primes=new ArrayList<>();
        for (int i = 2; i<100000 ; i++) {
            if(seive[i]==0){
                primes.add(i);
                for (long j = 1L*i*i; j <100000 ; j+=i) {
                    seive[(int)j]=1;
                }
            }
        }

        HashSet<Integer> badPrimeSet=new HashSet<>();
        for (int i = 0; i <m ; i++) {
            badPrimeSet.add(sc.nextInt());
        }
        
        int div=1;
        for (int i = n-1; i >=0 ; i--) {
            preGCD[i]/=div;
            int g=f(preGCD[i],primes,badPrimeSet);
            if(g<0)div*=preGCD[i];
            a[i]/=div;
        }

        int sum=0;
        for (int i = 0; i <n ; i++) {
            sum+=f(a[i],primes,badPrimeSet);
        }
        out.println(sum);

        out.close();
    }



}