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;
void err(istream_iterator<string> it) {}
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << ' ' << *it << " = " << a;
  err(++it, args...);
}
template <typename T, typename U>
inline void min_self(T& x, U y) {
  if (y < x) x = y;
}
template <typename T, typename U>
inline void max_self(T& x, U y) {
  if (x < y) x = y;
}
template <class T1, class T2>
ostream& operator<<(ostream& out, pair<T1, T2> pair) {
  return out << "(" << pair.first << ", " << pair.second << ")";
}
template <class T>
ostream& operator<<(ostream& out, vector<T> vec) {
  for (auto& v : vec) out << v << ' ';
  return out << "\n";
}
template <class T>
ostream& operator<<(ostream& out, set<T> vec) {
  out << "(";
  for (auto& v : vec) out << v << ", ";
  return out << ")";
}
template <class L, class R>
ostream& operator<<(ostream& out, map<L, R> vec) {
  out << "(";
  for (auto& v : vec) out << "[" << v.first << ", " << v.second << "]";
  return out << ")";
}
template <class A, class B>
istream& operator>>(istream& in, pair<A, B>& a) {
  return in >> a.first >> a.second;
}
template <class A>
istream& operator>>(istream& in, vector<A>& a) {
  for (A& i : a) in >> i;
  return in;
}
template <class Container>
void split(const std::string& str, Container& cont, char delim = ',') {
  stringstream ss(str);
  string token;
  while (std::getline(ss, token, delim)) {
    cont.push_back(token);
  }
}
long long px[4] = {-1, 0, 1, 0};
long long py[4] = {0, -1, 0, 1};
struct edge {
  long long u, v, wt;
  edge(long long a = 0, long long b = 0, long long c = 0) : u(a), v(b), wt(c) {}
  bool operator<(edge const& other) { return wt < other.wt; }
  friend ostream& operator<<(ostream& out, const edge& x) {
    return out << "(" << x.u << ", " << x.v << ", " << x.wt << ")";
  }
};
long long calc(long long num, long long parts, bool mode = true) {
  long long quo = num / parts + 1;
  long long rem = num % parts;
  long long nt1 = rem, nt2 = parts - rem;
  long long ans;
  if (mode) {
    ans = calc(num, parts - 1, false) - calc(num, parts, false);
  } else {
    ans = nt1 * quo * quo + nt2 * (quo - 1) * (quo - 1);
  }
  return ans;
}
void abcd() {
  long long n, k, res = 0;
  cin >> n >> k;
  priority_queue<pair<long long, pair<long long, long long>>> pq;
  for (long long i = 1; i <= n; i++) {
    long long x;
    cin >> x;
    pq.push({calc(x, 2), {x, 1}});
  }
  k = k - n;
  for (long long i = 1; i <= k; i++) {
    long long prev = pq.top().first;
    auto [num, parts] = pq.top().second;
    pq.pop();
    pq.push({calc(num, parts + 2), {num, parts + 1}});
  }
  while (!pq.empty()) {
    auto [num, parts] = pq.top().second;
    res += calc(num, parts, false);
    pq.pop();
  }
  cout << res << '\n';
  return;
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long t = 1;
  while (t--) {
    abcd();
  }
  return 0;
}
