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().solve();
	}
	
	void solve(){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int x=sc.nextInt();
		int[]a=new int[n];
		for(int i=0;i<n;i++){
			a[i]=sc.nextInt();
		}
		int sum_time=Integer.MAX_VALUE;
		int[] b=new int[n];
		Arrays.fill(b,Integer.MAX_VALUE);
		
		for(int k=0;k<n;k++){
			for(int i=0;i<n;i++){
				for(int j=0;j<=k;j++){
					if(i-j<0){
						b[i]=Math.min(b[i], a[i-j+n]);
					}else{
						b[i]=Math.min(b[i], a[i-j]);
					}
				}
			}
			int sum=0;
			for(int i=0;i<n;i++){
				sum+=b[i];
			}
			sum+=k*x;
			if(sum<sum_time)sum_time=sum;
		}
		System.out.println(sum_time);
		
	}

}