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;
using ll = long long;
ll func(int num, int ct) {
  ll sm = 0;
  ll part = num / ct;
  ll re = num % ct;
  sm += ((ct - re) * part * part);
  sm += (re * (part + 1) * (part + 1));
  return sm;
}
int main() {
  ios::sync_with_stdio(0), cin.tie(0);
  ;
  int n, k;
  cin >> n >> k;
  vector<ll> ar(n);
  ll cost = 0;
  priority_queue<tuple<ll, ll, ll>> pq;
  for (int i = 0; i < n; i++) {
    cin >> ar[i];
    cost += (ar[i] * ar[i]);
    pq.push({func(ar[i], 1) - func(ar[i], 2), 2, i});
  }
  while (n++ < k) {
    ll diff, part, index;
    tie(diff, part, index) = pq.top();
    pq.pop();
    cost -= diff;
    pq.push(
        {func(ar[index], part) - func(ar[index], part + 1), part + 1, index});
  }
  cout << cost;
}
