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.nextInt();
		int[][] arr = new int[n][n];
		long[] totals = new long[n];
		for (int i = 0; i < n; i++) {
		    arr[0][i] = sc.nextInt();
		    totals[0] += arr[0][i];
		}
		for (int i = 1; i < n; i++) {
		    for (int j = 0; j < n; j++) {
		        arr[i][j] = Math.min(arr[i - 1][j], arr[i - 1][(j - 1 + n) % n]);
		        totals[i] += arr[i][j];
		    }
		    totals[i] += x * i;
		}
		Arrays.sort(totals);
		System.out.println(totals[0]);
   }
}


