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;
const int inf = 1e9;
const long long int linf = 1LL << 50;
const double EPS = 1e-10;
int main(int argc, char const* argv[]) {
  int n;
  long long int x;
  cin >> n >> x;
  vector<long long int> a;
  for (int i = 0; i < n; i++) {
    long long int y;
    cin >> y;
    a.push_back(y);
  }
  long long int res = 0;
  long long int xmaxi = 0;
  for (int i = 0; i < n; i++) {
    long long int mini = a[i];
    int at = i;
    for (int j = 0; j < n; j++) {
      int sub = n - j + i;
      if (sub >= n) sub -= n;
      if (mini > sub * x + a[j]) {
        mini = sub * x + a[j];
        at = j;
      } else if (mini == sub * x + a[j]) {
        if (a[at] > a[j]) {
          at = j;
        }
      }
    }
    res += a[at];
    xmaxi = max(xmaxi, mini - a[at]);
  }
  res += xmaxi;
  cout << res << endl;
  return 0;
}
