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 N, x;
int a[100010];
int main() {
  cin >> N >> x;
  int ans = 0;
  for (int i = 0; i < N; i++) {
    cin >> a[i];
  }
  for (int i = 0; i < N; i++) {
    int mi = a[i];
    if (N >= 4) {
      int l = (i == 0 ? N - 1 : i - 1), r = (i == N - 1 ? 0 : i + 1);
      int n = 1;
      while (abs(l - r) > 1 && !(l == 0 && r == N - 1)) {
        mi = min(mi, min(x * n + a[l], x * n + a[r]));
        n++;
        l--;
        r++;
        if (l < 0) l = N - 1;
        if (r > N - 1) r = 0;
      }
    } else if (N == 3) {
      for (int j = 0; j < 3; j++) {
        if (i != j) {
          mi = min(x + a[j], mi);
        }
      }
    } else {
      if (i == 1)
        mi = min(a[i], x + a[i - 1]);
      else
        mi = min(a[i], x + a[i + 1]);
    }
    ans += mi;
  }
  cout << ans;
  return 0;
}
