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>
std::mt19937_64 rng(
    std::chrono::steady_clock::now().time_since_epoch().count());
long long int myRand(long long int R) {
  long long int val = rng() % R;
  assert(val >= 0);
  return val;
}
const long double PI = atan(1.0) * 4;
const int32_t INF32 = 2e9 + 7;
const int64_t INF64 = 3e18;
const int32_t LOG = 21;
const int32_t MOD = 1e9 + 7;
using namespace std;
void my_debugger(string second, long long int LINE_NUM) { cerr << '\n'; }
template <typename start, typename... end>
void my_debugger(string second, long long int LINE_NUM, start x, end... y) {
  if (second.back() != ',') {
    second += ',';
    cerr << "LINE(" << LINE_NUM << "): ";
  }
  long long int i = second.find(',');
  cerr << second.substr(0, i) << " = " << x;
  second = second.substr(i + 1);
  if (!second.empty()) cerr << ", ";
  my_debugger(second, LINE_NUM, y...);
}
long long int cost(long long int x, long long int cuts) {
  long long int val1 = x / cuts;
  long long int rem = x % cuts;
  long long int val2 = val1 + 1;
  long long int ans = val1 * val1 * (cuts - rem) + val2 * val2 * rem;
  return ans;
}
int32_t main() {
  ios_base::sync_with_stdio(false), cin.tie(nullptr);
  long long int tests = 1;
  for (long long int ii = 0; ii < (long long int)tests; ii++) {
    long long int n, k;
    cin >> n >> k;
    long long int a[n];
    for (long long int i = 0; i < (long long int)n; i++) cin >> a[i];
    priority_queue<tuple<long long int, long long int, long long int>> pq;
    long long int ans = 0;
    for (long long int i = 0; i < (long long int)n; i++) {
      ans += (a[i] * a[i]);
      long long int sub = cost(a[i], 1) - cost(a[i], 2);
      pq.push({sub, a[i], 1});
    }
    long long int cur = n;
    while (cur < k) {
      cur++;
      tuple<long long int, long long int, long long int> t = pq.top();
      pq.pop();
      long long int toSub, x, cuts;
      tie(toSub, x, cuts) = t;
      ans -= toSub;
      cuts++;
      pq.push({cost(x, cuts) - cost(x, cuts + 1), x, cuts});
    }
    cout << ans << '\n';
  }
  return 0;
}
