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;
template <typename T, typename U>
ostream& operator<<(ostream& out, const pair<T, U>& p) {
  out << '{' << p.first << ':' << p.second << '}';
  return out;
}
template <
    template <typename, typename...> class Container, typename Value,
    typename... AddParams,
    typename std::enable_if<!std::is_same<Container<Value, AddParams...>,
                                          std::string>::value>::type* = nullptr>
ostream& operator<<(ostream& out,
                    const Container<Value, AddParams...>& container) {
  out << '{';
  bool f = true;
  for (auto& i : container) {
    if (!f)
      out << ", ";
    else
      f = false;
    out << i;
  }
  out << '}';
  return out;
}
template <typename Arg1>
void _debug(const char* name, Arg1&& arg1) {
  cerr << name << " : " << arg1 << ')' << '\n';
}
template <typename Arg1, typename... Args>
void _debug(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << " : " << arg1 << " | ";
  while (*comma == ',' || *comma == ' ') ++comma;
  _debug(comma, args...);
}
const int N = 1e6 + 10;
struct Carrot {
  long long slices = 1;
  long long n = 0;
  Carrot() {}
  Carrot(long long no) { n = no; }
};
long long score(int n, int k) {
  if (n <= k) return n;
  long long rem = n % k;
  long long q = n / k;
  return (q + 1) * (q + 1) * (rem) + q * q * (k - rem);
}
long long increase(Carrot c) {
  return score(c.n, c.slices) - score(c.n, c.slices + 1);
}
bool operator<(const Carrot& c1, const Carrot& c2) {
  return increase(c1) < increase(c2);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n, k;
  cin >> n >> k;
  priority_queue<Carrot> Q;
  for (int i = 0; i < (n); i++) {
    int q;
    cin >> q;
    Q.push(Carrot(q));
  }
  for (int i = 0; i < k - n; i++) {
    auto t = Q.top();
    Q.pop();
    t.slices += 1;
    Q.push(t);
  }
  long long ans = 0;
  while (Q.size()) {
    auto t = Q.top();
    Q.pop();
    ;
    ans += score(t.n, t.slices);
  }
  cout << ans << '\n';
}
