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() {
  double x, a[10000] = {0}, ans = 0, min = 5000000000000, k;
  int n, r, i, j, b[10000] = {0}, c[10000] = {0}, max = -1;
  cin >> n >> x;
  for (i = 1; i <= n; i++) {
    cin >> a[i];
  }
  for (i = 1; i <= n; i++) {
    for (j = 0; j <= n - 1; j++) {
      r = (i + j) % n;
      if (r == 0) {
        r = n;
      }
      k = a[r] + x * j;
      if (k < min) {
        min = k;
        b[i] = a[r];
        c[i] = j;
      }
    }
  }
  for (i = 1; i <= n; i++) {
    if (max < c[i]) {
      max = c[i];
    }
  }
  for (i = 1; i <= n; i++) {
    ans = ans + b[i];
  }
  ans = ans + max * x;
  cout << ans << "\n";
}
