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>
const int mod = 1e9 + 7;
const int gmod = 2;
const int inf = 1039074182;
const double eps = 1e-9;
const long long llinf = 1LL * inf * inf;
template <typename T1, typename T2>
inline void chmin(T1 &x, T2 b) {
  if (b < x) x = b;
}
template <typename T1, typename T2>
inline void chmax(T1 &x, T2 b) {
  if (b > x) x = b;
}
inline void chadd(int &x, int b) {
  x += b - mod;
  x += (x >> 31 & mod);
}
template <typename T1, typename T2>
inline void chadd(T1 &x, T2 b) {
  x += b;
  if (x >= mod) x -= mod;
}
template <typename T1, typename T2>
inline void chmul(T1 &x, T2 b) {
  x = 1LL * x * b % mod;
}
template <typename T1, typename T2>
inline void chmod(T1 &x, T2 b) {
  x %= b, x += b;
  if (x >= b) x -= b;
}
template <typename T>
inline T mabs(T x) {
  return (x < 0 ? -x : x);
}
using namespace std;
using namespace std;
template <typename T>
ostream &operator<<(ostream &cout, vector<T> vec) {
  cout << "{";
  for (int i = 0; i < (int)vec.size(); i++) {
    cout << vec[i];
    if (i != (int)vec.size() - 1) cout << ',';
  }
  cout << "}";
  return cout;
}
template <typename T>
void operator*=(vector<T> &vec, int k) {
  for (auto &x : vec) x *= k;
}
template <typename T>
void operator-=(vector<T> &a, const vector<T> &b) {
  assert(a.size() == b.size());
  for (size_t it = 0; it < a.size(); it++) {
    a[it] -= b[it];
  }
}
template <typename T>
vector<T> operator*(const vector<T> &vec, int k) {
  vector<T> res(vec);
  res *= k;
  return res;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &cout, pair<T1, T2> p) {
  cout << "(" << p.first << ',' << p.second << ")";
  return cout;
}
template <typename T, typename T2>
ostream &operator<<(ostream &cout, set<T, T2> s) {
  vector<T> t;
  for (auto x : s) t.push_back(x);
  cout << t;
  return cout;
}
template <typename T>
ostream &operator<<(ostream &cout, multiset<T> s) {
  vector<T> t;
  for (auto x : s) t.push_back(x);
  cout << t;
  return cout;
}
template <typename T>
ostream &operator<<(ostream &cout, queue<T> q) {
  vector<T> t;
  while (q.size()) {
    t.push_back(q.front());
    q.pop();
  }
  cout << t;
  return cout;
}
template <typename T1, typename T2, typename T3>
ostream &operator<<(ostream &cout, map<T1, T2, T3> m) {
  for (auto &x : m) {
    cout << "Key: " << x.first << ' ' << "Value: " << x.second << endl;
  }
  return cout;
}
template <typename T>
T operator*(vector<T> v1, vector<T> v2) {
  assert(v1.size() == v2.size());
  int n = v1.size();
  T res = 0;
  for (int i = 0; i < n; i++) {
    res += v1[i] * v2[i];
  }
  return res;
}
template <typename T1, typename T2>
pair<T1, T2> operator+(pair<T1, T2> x, pair<T1, T2> y) {
  return make_pair(x.first + y.first, x.second + y.second);
}
template <typename T1, typename T2>
void operator+=(pair<T1, T2> &x, pair<T1, T2> y) {
  x.first += y.first;
  x.second += y.second;
}
template <typename T1, typename T2>
pair<T1, T2> operator-(pair<T1, T2> x) {
  return make_pair(-x.first, -x.second);
}
template <typename T>
vector<vector<T> > operator~(vector<vector<T> > vec) {
  vector<vector<T> > v;
  int n = vec.size(), m = vec[0].size();
  v.resize(m);
  for (int i = 0; i < m; i++) {
    v[i].resize(n);
  }
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < n; j++) {
      v[i][j] = vec[j][i];
    }
  }
  return v;
}
void print0x(int x) {
  std::vector<int> vec;
  while (x) {
    vec.push_back(x & 1);
    x >>= 1;
  }
  std::reverse(vec.begin(), vec.end());
  for (int i = 0; i < (int)vec.size(); i++) {
    std::cout << vec[i];
  }
  std::cout << ' ';
}
template <typename T>
void print0x(T x, int len) {
  std::vector<int> vec;
  while (x) {
    vec.push_back(x & 1);
    x >>= 1;
  }
  reverse(vec.begin(), vec.end());
  for (int i = vec.size(); i < len; i++) {
    putchar('0');
  }
  for (int i = 0; i < vec.size(); i++) {
    std::cout << vec[i];
  }
  std::cout << ' ';
}
using namespace std;
int n, k;
int a[100005];
vector<long long> vec;
inline long long calc(int pos, int b) {
  long long x = a[pos];
  long long base = x / b;
  long long rm = x - base * b;
  return base * base * (b - rm) + (base + 1) * (base + 1) * rm;
}
int main() {
  cin >> n >> k;
  k -= n;
  for (int i = 0; i < n; i++) {
    scanf("%d", a + i);
  }
  sort(a, a + n);
  long long res = 0;
  for (int i = 0; i < n; i++) {
    long long sum = calc(i, 1);
    res += sum;
    for (int j = 1; j <= min(k, a[i]); j++) {
      if (j * (n - i) > k) break;
      vec.push_back(sum - calc(i, j + 1));
      sum = calc(i, j + 1);
    }
  }
  sort(vec.begin(), vec.end());
  reverse(vec.begin(), vec.end());
  for (int i = 0; i < k; i++) {
    res -= vec[i];
  }
  cout << res << endl;
  return 0;
}
