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 b[2001][2001];
int main(void) {
  int n;
  int x;
  int a[2001];
  int c[2001] = {};
  long long int count = 0;
  cin >> n >> x;
  for (int i = (1); i <= (n); i++) {
    cin >> a[i];
  }
  for (int i = (1); i <= (n); i++) {
    b[0][i] = a[i];
    c[0] += a[i];
  }
  for (int k = (1); k <= (n - 1); k++) {
    int d = 0;
    for (int i = (1); i <= (n); i++) {
      int q;
      if (i - k > 0) {
        b[k][i] = min(b[k - 1][i], a[i - k]);
      } else {
        q = k - i;
        b[k][i] = min(b[k - 1][i], a[n - q]);
      }
      d += b[k][i];
    }
    c[k] = k * x + d;
  }
  int r = 1e9 + 1;
  for (int i = (0); i <= (n - 1); i++) {
    r = min(r, c[i]);
  }
  cout << r << endl;
  return 0;
}
