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) {
  try (Scanner sc = new Scanner(System.in)) {
   int N = sc.nextInt();
   int x = sc.nextInt();
   sc.nextLine();

   int[] as = new int[N];
   for (int i = 0; i < N; i++) {
    as[i] = sc.nextInt();
   }

   int min = Integer.MAX_VALUE;
   int minI = -1;

   for (int i = 0; i < N; i++) {
    if (as[i] < min) {
     min = as[i];
     minI = i;
    }
   }

   long ans = min;
   int i = (minI + 1) % N;
   while (i != minI) {
    if (as[i] < min + x) {
     ans += as[i];
    } else {
     ans += min + x;
    }
    i = (i + 1) % N;
   }
   System.out.println(ans);
  }
 }
}