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;
int n, m, a[100005];
long long ans;
long long W1(int x, int y) {
  int t1 = x / y, t2 = x % y;
  return 1ll * t1 * t1 * (y - t2) + 1ll * (t1 + 1) * (t1 + 1) * t2;
}
long long W2(int x, int y) { return W1(x, y) - W1(x, y + 1); }
struct Node {
  int x, y;
  long long vl;
  bool operator<(Node t) const { return vl < t.vl; }
};
priority_queue<Node> q;
int main() {
  scanf("%d %d", &n, &m);
  m -= n;
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &a[i]);
    ans += 1ll * a[i] * a[i];
    q.push((Node){a[i], 1, W2(a[i], 1)});
  }
  for (int i = 1; i <= m; ++i) {
    Node t = q.top();
    q.pop();
    ans -= t.vl;
    q.push((Node){t.x, t.y + 1, W2(t.x, t.y + 1)});
  }
  printf("%lld\n", ans);
  return 0;
}
