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.Arrays;
import java.util.Scanner;

public class Main {

	public static Scanner sc;
	
	public static void main(String[] args) {
		sc = new Scanner(System.in);
		
		int n = sc.nextInt();
		int x = sc.nextInt();
		
		int []a = new int[n];
		int []b = new int[n];
		
		for(int i=0; i<n; i++){
			a[i] = sc.nextInt();
			b[i] = a[i];
		}
		Arrays.sort(b);
		
		int ans = Integer.MAX_VALUE;
		int temp = 0;
		for(int k=0; k<n; k++){
			for(int i=0; i<n; i++){
				temp = k*x + b[0]*k;
				for(int j=0; j<n-k; j++){
					temp+=b[(i+j)%n];
				}
				ans = Math.min(ans, temp);
			}
		}
		
		System.out.println(ans);
	}

}
