#include <bits/stdc++.h>
using namespace std;
const int Maxn = 5005;
const int Maxm = 100005;
bool nprime[Maxm];
vector<int> pr;
bool bad[Maxm];
set<int> B;
int n, m;
int a[Maxn];
int g[Maxn], best[Maxn];
int delt[Maxn];
int sum, bdelt;
int gcd(int x, int y) { return x ? gcd(y % x, x) : y; }
int main() {
  for (int i = 2; i < Maxm; i++)
    if (!nprime[i]) {
      pr.push_back(i);
      for (int j = i + i; j < Maxm; j += i) nprime[j] = true;
    }
  scanf("%d %d", &n, &m);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  for (int i = 0; i < m; i++) {
    int b;
    scanf("%d", &b);
    if (b < Maxm)
      bad[b] = true;
    else
      B.insert(b);
  }
  for (int i = 1; i <= n; i++) {
    int num = a[i];
    for (int j = 0; pr[j] * pr[j] <= num; j++)
      if (num % pr[j] == 0)
        if (bad[pr[j]]) do {
            sum--;
            num /= pr[j];
          } while (num % pr[j] == 0);
        else
          do {
            sum++;
            num /= pr[j];
          } while (num % pr[j] == 0);
    if (num > 1)
      if (num < Maxm)
        sum += bad[num] ? -1 : 1;
      else
        sum += B.count(num) ? -1 : 1;
    g[i] = gcd(g[i - 1], a[i]);
  }
  for (int i = n; i >= 1; i--) {
    int num = g[i];
    delt[i] = 0;
    for (int j = 0; pr[j] * pr[j] <= num; j++)
      if (num % pr[j] == 0)
        if (bad[pr[j]]) do {
            delt[i]++;
            num /= pr[j];
          } while (num % pr[j] == 0);
        else
          do {
            delt[i]--;
            num /= pr[j];
          } while (num % pr[j] == 0);
    if (num > 1)
      if (num < Maxm)
        delt[i] += bad[num] ? 1 : -1;
      else
        delt[i] += B.count(num) ? 1 : -1;
    best[i] = delt[i] * i;
    for (int j = i + 1; j <= n; j++)
      best[i] = max(best[i], (delt[i] - delt[j]) * i + best[j]);
    bdelt = max(bdelt, best[i]);
  }
  printf("%d\n", sum + bdelt);
  return 0;
}
