There are some rabbits in Singapore Zoo. To feed them, Zookeeper bought n carrots with lengths a_1, a_2, a_3, …, a_n. However, rabbits are very fertile and multiply very quickly. Zookeeper now has k rabbits and does not have enough carrots to feed all of them. To solve this problem, Zookeeper decided to cut the carrots into k pieces. For some reason, all resulting carrot lengths must be positive integers.

Big carrots are very difficult for rabbits to handle and eat, so the time needed to eat a carrot of size x is x^2.

Help Zookeeper split his carrots while minimizing the sum of time taken for rabbits to eat the carrots.

Input

The first line contains two integers n and k (1 ≤ n ≤ k ≤ 10^5): the initial number of carrots and the number of rabbits.

The next line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6): lengths of carrots.

It is guaranteed that the sum of a_i is at least k.

Output

Output one integer: the minimum sum of time taken for rabbits to eat carrots.

Examples

Input


3 6
5 3 1


Output


15


Input


1 4
19


Output


91

Note

For the first test, the optimal sizes of carrots are \{1,1,1,2,2,2\}. The time taken is 1^2+1^2+1^2+2^2+2^2+2^2=15

For the second test, the optimal sizes of carrots are \{4,5,5,5\}. The time taken is 4^2+5^2+5^2+5^2=91.
#include <bits/stdc++.h>
using namespace std;
long long calc(long long a, int from) {
  long long e = a / from;
  long long add = a % from;
  return e * e * (from - add) + (e + 1) * (e + 1) * add;
}
long long get(long long a, int from) {
  if (a < from) {
    return -1;
  }
  return calc(a, from) - calc(a, from + 1);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  int n, k;
  cin >> n >> k;
  long long res = 0;
  multiset<pair<long long, pair<int, int>>> carrots;
  for (int i = 0; i < n; i++) {
    long long e;
    cin >> e;
    res += 1LL * e * e;
    carrots.insert(make_pair(-get(e, 1), make_pair(e, 1)));
  }
  for (int i = 0; i < k - n; i++) {
    auto it = carrots.begin();
    carrots.erase(carrots.begin());
    res += it->first;
    auto p = it->second;
    p.second++;
    carrots.insert(
        make_pair(-get(p.first, p.second), make_pair(p.first, p.second)));
  }
  cout << res << endl;
  return 0;
}
