Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.

Snuke can perform the following two actions:

* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.

* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.




Find the minimum time that Snuke needs to have slimes in all N colors.

Constraints

* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9

Input

The input is given from Standard Input in the following format:


N x
a_1 a_2 ... a_N


Output

Find the minimum time that Snuke needs to have slimes in all N colors.

Examples

Input

2 10
1 100


Output

12


Input

3 10
100 1 100


Output

23


Input

4 10
1 2 3 4


Output

10
#include <bits/stdc++.h>
using namespace std;
int main(void) {
  unsigned long long n, x, l = 0, s = 1e11;
  int si = 0;
  cin >> n >> x;
  vector<pair<unsigned long long, int> > a;
  unsigned long long in, ret = 0;
  for (int i = 0; i < n; i++) {
    cin >> in;
    if (s > in) {
      s = in;
      si = i;
    }
    ret += in;
    if (x > in)
      ;
    else {
      a.push_back(make_pair(in, i));
    }
  }
  long long mi = 1e10, ma = 0;
  for (int i = 0; i < a.size(); i++) {
    mi = min(mi, (long long)((si - a[i].second) * x));
    ma = max(ma, (long long)((a[i].second - si) * x));
  }
  if (a.size() == 1) ma = 0;
  sort(a.begin(), a.end());
  unsigned long long guchoku = (ma - mi) + s * n;
  cout << min(guchoku, ret) << endl;
}
