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 void main(String[] args){
		new Main().run();
	}

	long[] a;
	long a1;
	int n;
	int x;
	
	void run(){
		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.nextLong();
		}
		a1 = a[0];
		Arrays.sort(a);
		
		long asum = 0;
		long xmax = 0;
		for(int i=0;i<n;i++){
			long tmp = a[i];
			int tmp4 = i;
			for(int j=0;j<n;j++){
				long tmp3 = 0;
				if(i>j){
					tmp3 = i-j;
				}else if(j>i){
					tmp3 = n-(j-i);
				}
				long tmp2 = a[j] + x*tmp3;
				if(tmp2<tmp){
					tmp = tmp2;
					tmp4 = j;
					xmax = Math.max(xmax, tmp3);
				}
			}
			asum += a[tmp4];
		}
		
		System.out.println(asum+x*xmax);
	}

}
