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.Scanner;

public class Main {
  static final long INF = Long.MAX_VALUE / 2;
  static int n;
  static long x;
  static long[] a;

  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);

    n = sc.nextInt(); x = sc.nextInt();
    a = new long[n];
    for(int i = 0; i < n; i++){
      a[i] = sc.nextInt();
    }

    long sum = 0;
    for(int i = 0; i < n; i++){
      long min = INF;
      for(int j = 0; j < n; j++){
        if(i > j){
          min = Math.min(min, a[j] + (long)(i - j) * x);
        }
        else{
          min = Math.min(min, a[j] + (long)(j - i) * x);
        }
      }
      sum += min;
    }

    System.out.println(sum);
  }
}