Arpa has found a list containing n numbers. He calls a list bad if and only if it is not empty and gcd (see notes section for more information) of numbers in the list is 1.

Arpa can perform two types of operations:

  * Choose a number and delete it with cost x. 
  * Choose a number and increase it by 1 with cost y. 



Arpa can apply these operations to as many numbers as he wishes, and he is allowed to apply the second operation arbitrarily many times on the same number.

Help Arpa to find the minimum possible cost to make the list good.

Input

First line contains three integers n, x and y (1 ≤ n ≤ 5·105, 1 ≤ x, y ≤ 109) — the number of elements in the list and the integers x and y.

Second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the elements of the list.

Output

Print a single integer: the minimum possible cost to make the list good.

Examples

Input

4 23 17
1 17 17 16


Output

40


Input

10 6 2
100 49 71 73 66 96 8 60 41 63


Output

10

Note

In example, number 1 must be deleted (with cost 23) and number 16 must increased by 1 (with cost 17).

A gcd (greatest common divisor) of a set of numbers is the maximum integer that divides all integers in the set. Read more about gcd [here](https://en.wikipedia.org/wiki/Greatest_common_divisor).
#include <bits/stdc++.h>
using namespace std;
long long dot(pair<long long, long long> u, pair<long long, long long> v) {
  return u.first * v.first + u.second * v.second;
}
long long cross(pair<long long, long long> u, pair<long long, long long> v) {
  return u.first * v.second - u.second * v.first;
}
long long ccw(pair<long long, long long> u, pair<long long, long long> v) {
  long long val = cross(u, v);
  if (val > 0)
    return 1;
  else if (val == 0)
    return 0;
  else
    return -1;
}
pair<long long, long long> vec(pair<long long, long long> a,
                               pair<long long, long long> b) {
  return pair<long long, long long>(b.first - a.first, b.second - a.second);
}
pair<long long, long long> O;
bool cmpAngle(pair<long long, long long> A, pair<long long, long long> B) {
  pair<long long, long long> OA = vec(O, A);
  pair<long long, long long> OB = vec(O, B);
  if (ccw(OA, OB) == 0)
    return dot(OA, OA) < dot(OB, OB);
  else
    return ccw(OA, OB) > 0;
}
vector<pair<long long, long long> > convexHull(
    vector<pair<long long, long long> >& point) {
  vector<pair<long long, long long> > hull;
  sort(point.begin(), point.end());
  O = point[0];
  sort(point.begin() + 1, point.end(), cmpAngle);
  vector<pair<long long, long long> > checker;
  checker.push_back(O);
  for (long long i = 1; i < point.size(); i++) {
    while (i + 1 < point.size() &&
           ccw(vec(O, point[i]), vec(O, point[i + 1])) == 0)
      ++i;
    checker.push_back(point[i]);
  }
  if (checker.size() < 3) return hull;
  hull.push_back(O);
  hull.push_back(point[1]);
  for (long long i = 2; i < checker.size(); i++) {
    while (true) {
      pair<long long, long long> curr = hull.back();
      hull.pop_back();
      pair<long long, long long> prev = hull.back();
      hull.push_back(curr);
      pair<long long, long long> next = checker[i];
      if (ccw(vec(prev, curr), vec(prev, next)) == 1) {
        hull.push_back(next);
        break;
      } else
        hull.pop_back();
    }
  }
  return hull;
}
pair<double, double> solve(long long A, long long B, long long E, long long C,
                           long long D, long long F) {
  long long Det = A * D - B * C;
  long long DetX = E * D - B * F;
  long long DetY = A * F - C * E;
  if (Det == 0)
    return pair<double, double>(1e18, 1e18);
  else {
    return pair<double, double>(DetX / double(Det), DetY / double(Det));
  }
}
vector<long long> P;
vector<long long> R;
void init(long long n) {
  R = vector<long long>(n);
  P = vector<long long>(n);
  for (long long i = 0; i < n; i++) {
    P[i] = i;
  }
}
long long root(long long x) {
  if (P[x] != x) return P[x] = root(P[x]);
  return P[x];
}
void link(long long x, long long y) {
  long long rx = root(x);
  long long ry = root(y);
  if (R[rx] > R[ry]) swap(rx, ry);
  P[rx] = ry;
  if (R[rx] == R[ry]) ++R[ry];
}
void update(long long node, long long left, long long right, long long pos,
            long long val, vector<long long>& tree) {
  if (left == right)
    tree[node] = val;
  else {
    long long mid = (left + right) / 2;
    if (pos <= mid)
      update(2 * node + 1, left, mid, pos, val, tree);
    else
      update(2 * node + 2, mid + 1, right, pos, val, tree);
    tree[node] = tree[2 * node + 1] + tree[2 * node + 2];
  }
}
long long query(long long node, long long left, long long right,
                long long start, long long end, vector<long long>& tree) {
  if (end < left && right < start)
    return 0;
  else if (start <= left && right <= end)
    return tree[node];
  else {
    long long mid = (left + right) / 2;
    long long p1 = query(2 * node + 1, left, mid, start, end, tree);
    long long p2 = query(2 * node + 2, mid + 1, right, start, end, tree);
    return p1 + p2;
  }
}
long long powerMod(long long b, long long p, long long m) {
  if (p == 0)
    return 1 % m;
  else if (p == 1)
    return b % m;
  else {
    long long tmp = powerMod(b, p / 2, m);
    tmp = (tmp * tmp) % m;
    if (p & 1)
      return (b % m * tmp) % m;
    else
      return tmp;
  }
}
long long multiplyMod(long long a, long long b, long long m) {
  if (b == 0)
    return 0;
  else if (b == 1)
    return a % m;
  else {
    if (b & 1)
      return (a % m + multiplyMod(a, b - 1, m)) % m;
    else
      return (2 % m * multiplyMod(a, b / 2, m)) % m;
  }
}
vector<long long> vec5(vector<long long>& a, vector<long long>& b) {
  vector<long long> ans(5);
  for (long long i = 0; i < 5; i++) {
    ans[i] = b[i] - a[i];
  }
  return ans;
}
long long dot5(vector<long long>& a, vector<long long>& b) {
  long long ans = 0;
  for (long long i = 0; i < 5; i++) {
    ans += a[i] * b[i];
  }
  return ans;
}
int main() {
  long long n, del, inc;
  cin >> n >> del >> inc;
  vector<long long> ar(n);
  vector<long long> cnt(2 * 1e6 + 10);
  vector<long long> sum(2 * 1e6 + 10);
  long long Max = 0;
  for (long long i = 0; i < n; i++) {
    cin >> ar[i];
    Max = max(ar[i], Max);
    cnt[ar[i]]++;
    sum[ar[i]] += ar[i];
  }
  for (long long i = 1; i <= 2 * 1e6; i++) {
    cnt[i] += cnt[i - 1];
    sum[i] += sum[i - 1];
  }
  long long ans = 1e18;
  for (long long gcd = 2; gcd <= 1e6; gcd++) {
    long long curr = 0;
    for (long long top = gcd; top <= 1e6 + gcd; top += gcd) {
      long long btm = top - gcd;
      long long mid = max(btm + 1, top - min(gcd, del / inc));
      if (btm <= mid - 1) {
        curr += del * (cnt[mid - 1] - cnt[btm]);
      }
      if (mid - 1 <= top - 1) {
        curr += inc * (top * (cnt[top - 1] - cnt[mid - 1]) -
                       (sum[top - 1] - sum[mid - 1]));
      }
    }
    ans = min(ans, curr);
  }
  cout << ans << endl;
}
