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
import java.util.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    long x = sc.nextLong();
    long[] a = new long[n];
    for(int i = 0; i < n; i++) {
      a[i] = sc.nextLong();
    }
    long[][] b = new long[n][n];
    for(int i = 0; i < n; i++) {
      b[i][0] = a[i];
      for(int j = 1; j < n; j++) {
        if((i - j) >= 0) {
          b[i][j] = Math.min(b[i][j - 1], a[i - j]);
        } else {
          b[i][j] = Math.min(b[i][j - 1], a[n - (j - i)]);
        }
      }
    }
    long ans = (long)Math.pow(10, 18);
    for(int k = 0; k < n; k++) {
      long t = (x * k);
      for(int i = 0; i < n; i++) {
        t += b[i][k];
      }
      ans = Math.min(ans, t);
    }
    System.out.println(ans);
  }
}