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>
namespace chtholly {
char buf[1 << 23], *p1 = buf, *p2 = buf;
inline int read() {
  int x = 0, f = 1;
  char c = getchar();
  for (; !isdigit(c); c = getchar()) f ^= c == '-';
  for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + (c ^ '0');
  return f ? x : -x;
}
template <typename mitsuha>
inline bool read(mitsuha &x) {
  x = 0;
  int f = 1;
  char c = getchar();
  for (; !isdigit(c) && ~c; c = getchar()) f ^= c == '-';
  if (!~c) return 0;
  for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + (c ^ '0');
  return x = f ? x : -x, 1;
}
template <typename mitsuha>
inline int write(mitsuha x) {
  if (!x) return 0 & putchar(48);
  if (x < 0) putchar('-'), x = -x;
  int bit[20], i, p = 0;
  for (; x; x /= 10) bit[++p] = x % 10;
  for (i = p; i; --i) putchar(bit[i] + 48);
  return 0;
}
inline char fuhao() {
  char c = getchar();
  for (; isspace(c); c = getchar())
    ;
  return c;
}
}  // namespace chtholly
using namespace chtholly;
using namespace std;
const int yuzu = 3e5;
struct node {
  long long a, b, c;
  bool operator<(const node &x) const { return a < x.a; }
};
priority_queue<node> q;
long long gv(long long a, long long b) {
  long long u = a / b, v = a - u * b;
  return (b - v) * u * u + v * (u + 1) * (u + 1);
}
int main() {
  int n, k, i;
  long long lxy = 0, t;
  read(n), read(k);
  for (i = 1; i <= n; ++i) {
    t = read(), lxy += t * t;
    q.push({gv(t, 1) - gv(t, 2), t, 2});
  }
  for (i = 1; i <= k - n; ++i) {
    lxy -= q.top().a;
    long long b = q.top().b, c = q.top().c;
    q.pop();
    q.push({gv(b, c) - gv(b, c + 1), b, c + 1});
  }
  printf("%lld\n", lxy);
}
