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;
const int maxn = 2e5 + 7;
const int mod = 1e9 + 7;
const long long INF = 1e18;
priority_queue<pair<long long, pair<long long, long long> > > Q;
long long cal(long long x, long long p) {
  long long a = x / p;
  long long b = x % p;
  return (p - b) * a * a + b * (a + 1) * (a + 1);
}
void rua() {
  int n, k;
  scanf("%d%d", &n, &k);
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    int x;
    scanf("%d", &x);
    ans += 1ll * x * x;
    Q.push({cal(x, 1) - cal(x, 2), {x, 2}});
  }
  int m = k - n;
  while (m--) {
    auto u = Q.top();
    Q.pop();
    ans -= u.first;
    int x = u.second.first, y = u.second.second;
    Q.push({cal(x, y) - cal(x, y + 1), {x, y + 1}});
  }
  printf("%lld\n", ans);
}
int main() {
  rua();
  return 0;
}
